From 8817a50c0e4953c679ec2d252e96395bd7da6300 Mon Sep 17 00:00:00 2001 From: Seppo Ingalsuo Date: Thu, 30 Jun 2022 21:01:39 +0300 Subject: [PATCH] Algorithms: Add equalizers design tutorial This patch adds a section about measuring acoustical speaker frequency response and design of IIR and FIR equalizers to improve it. Signed-off-by: Seppo Ingalsuo --- algos/eq/Picture_FIR_equalized_response.png | Bin 0 -> 65252 bytes algos/eq/Picture_FIR_impulse_response.png | Bin 0 -> 27728 bytes algos/eq/Picture_FIR_response.png | Bin 0 -> 53684 bytes algos/eq/Picture_FIR_response_absolute.png | Bin 0 -> 51106 bytes .../Picture_FIR_right_channel_equalized.png | Bin 0 -> 64622 bytes ...re_IIR_FIR_target_vs_achieved_response.png | Bin 0 -> 60473 bytes algos/eq/Picture_iir_absolute_response.png | Bin 0 -> 51470 bytes ...re_iir_filter_response_vs_ideal_target.png | Bin 0 -> 54469 bytes algos/eq/Picture_iir_impulse_response.png | Bin 0 -> 18649 bytes algos/eq/Picture_iir_poles_and_zeros.png | Bin 0 -> 23782 bytes ...r_simulated_left_and_channel_responses.png | Bin 0 -> 66006 bytes ...re_imported_frequency_response_for_iir.png | Bin 0 -> 65366 bytes algos/eq/Picture_raw_frequency_response.png | Bin 0 -> 67499 bytes algos/eq/Picture_response_with_smoothing.png | Bin 0 -> 66261 bytes ...re_right_channel_FIR_absolute_response.png | Bin 0 -> 50603 bytes algos/eq/Picture_right_channel_response.png | Bin 0 -> 65771 bytes ...e_simulated_IIR_FIR_frequency_response.png | Bin 0 -> 73901 bytes ...lated_left_and_right_channel_responses.png | Bin 0 -> 72551 bytes algos/eq/Picture_speaker_meas.jpg | Bin 0 -> 116075 bytes ...ture_tested_speaker_frequency_response.png | Bin 0 -> 66862 bytes algos/eq/equalizers_tuning.rst | 924 ++++++++++++++++++ algos/index.rst | 3 +- 22 files changed, 926 insertions(+), 1 deletion(-) create mode 100644 algos/eq/Picture_FIR_equalized_response.png create mode 100644 algos/eq/Picture_FIR_impulse_response.png create mode 100644 algos/eq/Picture_FIR_response.png create mode 100644 algos/eq/Picture_FIR_response_absolute.png create mode 100644 algos/eq/Picture_FIR_right_channel_equalized.png create mode 100644 algos/eq/Picture_IIR_FIR_target_vs_achieved_response.png create mode 100644 algos/eq/Picture_iir_absolute_response.png create mode 100644 algos/eq/Picture_iir_filter_response_vs_ideal_target.png create mode 100644 algos/eq/Picture_iir_impulse_response.png create mode 100644 algos/eq/Picture_iir_poles_and_zeros.png create mode 100644 algos/eq/Picture_iir_simulated_left_and_channel_responses.png create mode 100644 algos/eq/Picture_imported_frequency_response_for_iir.png create mode 100644 algos/eq/Picture_raw_frequency_response.png create mode 100644 algos/eq/Picture_response_with_smoothing.png create mode 100644 algos/eq/Picture_right_channel_FIR_absolute_response.png create mode 100644 algos/eq/Picture_right_channel_response.png create mode 100644 algos/eq/Picture_simulated_IIR_FIR_frequency_response.png create mode 100644 algos/eq/Picture_simulated_left_and_right_channel_responses.png create mode 100644 algos/eq/Picture_speaker_meas.jpg create mode 100644 algos/eq/Picture_tested_speaker_frequency_response.png create mode 100644 algos/eq/equalizers_tuning.rst diff --git a/algos/eq/Picture_FIR_equalized_response.png 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XGa(qayeGpDr*{OEfnv1BdX;NLb@aH7OQR9DMPCu%Aj zmfd(!pI@1o!=!|G8iV0JZ@(295QojVS$A^>5OJYd7dXKJb|?ifa5TA}B~r9)VUuwFa7l84 zXQ3+125t}sWKt%tgAvn1=JeL39|#wwqHd)6zn3=I9Iv)rj5pCl1QUFag|n$h^4#sc zGtTT28^x-EpUDawHRw{Qw-{#zzsHx2ci0>s0UOYX&IhmGwGP_^^~1{+%x~945-Hx{ z*c4nd>SQ5s^bKy^BLg?98CRTJJs@WwKI0G+FcD9Sa13N+aN)imDD`eBf&ua2Rl4-u zf|qVGX +digital. In both cases use of calibrated reference microphone is +needed. + +Preparations +************ + +The device should allow remote ssh without password for the automatic +scripts to work. Since the developers have usually their public and +private keys setup only this is needed. Find out the IP address from +ifconfig command output on your device. + +.. code-block:: bash + + ssh-copy-id -i ~/.ssh/id_rsa.pub user@aa.bb.cc.dd + +For ssh to work with low delay the development PC and tuned device +should be on the same local IP network. You can check that remote +playback works to DUT with example command: + +.. code-block:: bash + + ssh user@aa.bb.cc.dd "aplay -l" + +Since the tests are done with low-level ALSA aplay and arecord +utilities it is recommended to temporarily rename in DUT the audio +servers to disable them. Kill manually the processes or reboot to +avoid them continue running. The audio servers can be disabled from OS +system control in more elegant way but it is harder to remember how to +do it and restore to normal vs. the brute force way. + +.. code-block:: bash + + cd /usr/bin + sudo mv pulseaudio pulseaudio.disabled + sudo mv pipewire pipewire.disabled + + +Frequency response measurement +****************************** + +Note: More professional audio analyzer systems are recommended to be +used for final tuning. The procedures described in this document are +for coarse initial settings. Final tuning, especially if dependence +to regulations and standards need to be done with care in professional +environment with calibrated measurement equipment. + +To measure speakers an omnidirectional USB measurement microphone is +recommended, e.g. UMM6 [2]_ or UMIK-1 [3]_. Such microphones are +inexpensive and do not necessarily have a flat frequency response but +the manufacturers provide a serial number based downloadable +calibration file for them. The calibration can be applied to these +measurements in SOF as well by referencing the downloaded calibration +data to measurement script. + +Next step up are analog condenser measurement microphones with a +high-end USB sound card that can provide the 48V phantom voltage. But +analog microphones add more calibration consideration for analog +level. The measurement microphones can be also calibrated for absolute +level with dedicated microphone calibrators those can output into the +sealed compartment a reference 94 dBSPL tone. + +The tools for measurement and EQ design are in located in directory +$SOF_WORKSPACE/sof/tools/tune/eq. The test setup is such that the DUT +device plays back the measurement wav file via ssh commands and the +development PC connected USB microphone captures the output. To +achieve this the configuration files for playback and capture need to +be edited. + +The capture device UMM6 is hw:3.0 (card 3, device 0), this can be seen +from output of arecord command on a the development PC example. We +also know that this device supports one capture channel. + +.. code-block:: bash + + arecord -l + **** List of CAPTURE Hardware Devices **** + card 0: PCH [HDA Intel PCH], device 0: ALC257 Analog [ALC257 Analog] + Subdevices: 1/1 + Subdevice #0: subdevice #0 + card 1: Ultra [Fast Track Ultra], device 0: USB Audio [USB Audio] + Subdevices: 1/1 + Subdevice #0: subdevice #0 + card 2: Audio [ThinkPad Dock USB Audio], device 0: USB Audio [USB Audio] + Subdevices: 1/1 + Subdevice #0: subdevice #0 + card 3: UMM6 [UMM-6], device 0: USB Audio [USB Audio] + Subdevices: 1/1 + Subdevice #0: subdevice #0 + +The settings file + +.. code-block:: bash + + $ cat mls_rec_config.txt + %% Recording device configuration + + rec.ssh = 0; % Set to 1 for remote capture + rec.user = ''; % Set to user@domain for ssh + rec.dir = '/tmp'; % Directory for temporary files + rec.dev = 'hw:3,0'; % Audio capture device + rec.nch = 1; % Number audio capture channels to use + + % Use '' if calibration is not needed. Otherwise set to + % e.g. '1234567.txt'. Such calibration data format is supported for + % some reasonably priced measurement microphones. The ASCII text + % calibration data file is the measured frequency response of the used + % microphone. Lines in the beginning those start with character " are + % treated as comment. The successive lines should be + % number pairs. Their unit must be Hz and dB. + rec.cal = ''; + +Similarly check with remote aplay command the playback devices and +then edit the playback settings. + +.. code-block:: bash + + ssh user@aa.bb.cc.dd "aplay -l" + **** List of PLAYBACK Hardware Devices **** + card 0: sofglkda7219max [sof-glkda7219max], device 0: Speakers (*) [] + Subdevices: 1/1 + Subdevice #0: subdevice #0 + card 0: sofglkda7219max [sof-glkda7219max], device 1: Headset (*) [] + Subdevices: 1/1 + Subdevice #0: subdevice #0 + card 0: sofglkda7219max [sof-glkda7219max], device 5: HDMI1 (*) [] + Subdevices: 1/1 + Subdevice #0: subdevice #0 + card 0: sofglkda7219max [sof-glkda7219max], device 6: HDMI2 (*) [] + Subdevices: 1/1 + Subdevice #0: subdevice #0 + card 0: sofglkda7219max [sof-glkda7219max], device 7: HDMI3 (*) [] + Subdevices: 1/1 + Subdevice #0: subdevice #0 + +On the DUT the speakers are provided by device hw:0,0. It's known that +there's two playback channels in the device. + +.. code-block:: bash + + $ cat mls_play_config.txt + play.ssh = 1; % Set to use remote ssh commands + play.user = 'user@aa.bb.cc.dd'; % Set user@domain for ssh + play.dir = '/tmp'; % directory for temporary files + play.dev = 'hw:0,0'; % Audio device for playback + play.nch = 2; % Number of playback channels to test + +Next the measurement orientation and measurement microphone place is +considered. A notebook could be placed on top of a table symmetrically +where the measurement microphone location should be symmetrical to +display center axis. The microphone location could be near the center +of user’s ears. If the measurement microphone capture is too silent or +disturbed by ambient noise the microphone should be placed closer into +near field. + +.. figure:: Picture_speaker_meas.jpg + :width: 600 + + On-axis measurement position for bottom located speakers. + +Since this example device is a convertible type with a near 360 degree +display hinge there are several usage orientations. It was chosen to +measure the speakers from about their firing axis. Since the response +is impacted by orientation this was felt as safest choice. It also +gave the flattest looking frequency response. + +The MLS measurement tolerates some noise but the more silent the +environment is the better it is. An anechoic chamber would be ideal +naturally. The used MLS signal sets stress for the speakers so start +with a low volume setting with “alsamixer -Dhw:0”. Find the speaker +playback volume control PGA or volume controlin speaker amplifier and +start with e.g. 50%. + +Start Octave and launch the measurement + +.. code-block:: octave + + [f, m] = mls_freq_resp('DUT'); + +If the script warns about too silent audio increase the volume and/or +bring the microphone closer to the device. If the device has small +speakers and test signal playback sounds like at being near to their +capability limit, it is best to ignore the warning. The speakers may +permanently damage if the playback is too loud. + +If problems the script contains a self test for quick integrity +check. The self test measures a recursive filter that simulates a +non-flat response. The measurement and theoretical response that’s +computed directly from filter coefficients should match. + +.. code-block:: octave + + [f, m] = mls_freq_resp('selftest'); + +The test signal contains two chirps and a few times repeated +pseudo-random numbers sequence. The chirps are used to locate and +extract the MLS part. The MLS sequence has such a characteristic the +the correlation with itself is minimal. The sufficient length of the +sequence is used to suppress room reverberation from the +measurement. It provides nearly similar measured frequency responses +as achieved in anechoic conditions. As in anechoic chamber the setup +should be as much as possible like free-field. The desk/stand where +the device is measured should be away from reflecting surfaces. + +This MLS measurement would naturally also benefit from doing in +anechoic chamber since the MLS technique cannot eliminate all reverb +impact form measurement. Though usually in chambers there’s +professional equipment available like Audio Precision ® and other. If +such are available this measurement step with SOF can be avoided and +continued from next section for data import for tuning. + +.. figure:: Picture_raw_frequency_response.png + :width: 600 + + Frequency response measurement. The first channel is aligned to 0 + dB at 1 kHz. The second channel is shown with true offset + vs. first. + +After a successful measurement a plot with frequency (Hz) and +magnitude (dB) as x and y axis will be shown. The variable f will +contain the frequency response and variable m the magnitude. If the +number of measured channels was larger than 1 the m is a matrix. The +result can be saved for equalizer design into a .mat file. + +.. code-block:: octave + + save example_dut.mat f m + +Equalizer design +**************** + +It can be seen from the picture that the output of speakers is weak at +below 200 Hz. There’s two resonances, first at about 700 Hz and second +at about 5 kHz (better visible on table orientation). The response is +within -10 .. +10 dB in about 300 - 13000 Hz range. The equalization +should not be applied outside these frequencies to avoid a large loss +of SPL. It can be also seen that the left and right speaker have +slightly different frequency response. + +Next the measurement data is imported to SOF. It can be done by load +of previously saved file or importing e.g. in MS Excel format from +other equipment. The matrix columns for frequency and channel specific +levels need to be known. + +The tool in SOF is a set of functions to be used in user created +script. Therefore programming knowledge is needed. The benefit of +using script is the procedure is easy to repeat and documented by +itself. + +FIR equalizer +************* + +The finite impulse response (FIR) filter type has the advantages that +design for any finite time impulse response / frequency response is +simple and robust. The filters do not oscillate by design so the +rounding errors do not appear as noise. The rounding of coefficients +into a fixed word length only impairs slightly the response but the +effect can be usually ignored. Therefore the FIR equalizers especially +when used with 24 and 32 bit audio format are compatible with studio +like 24 bit audio quality. + +Due finite response (often limited by DSP resources) the FIR filters +are not practical for lowest frequencies unless very long filters are +used. The longer the filter is the more DSP RAM and MCPS the +processing consumes. However FIR filters are great for mid and high +frequencies equalization. The next example equalizes those frequencies +for the previously done measurement. + +The initial script for tuning is shown below. Alternatively for other +equipment the data import could be done in Excel format and use +function xlsread(); to read a matrix and then extract the frequency +and magnitude columns. + +.. code-block:: octave + + %% Load measurement data, variable f and m + load example_dut.mat; + + %% EQ settings + eq1 = eq_defaults(); % Get defaults + eq1.fs = 48e3; % Set sample rate + eq1.norm_type = 'loudness'; % Normalize criteria can be loudness/peak/1k + eq1.norm_offs_db = -3; % Offset in dB to normalize, -3dB loudness + eq1.logsmooth_plot = 1.0; % Smooth over 1.0 octaves + eq1.logsmooth_eq = 1.0; % Smooth over 1.0 octaves + eq1.enable_fir = 1; % By default both FIR and IIR disabled + eq1.fir_beta = 3.0; % Lower beta is more accurate but be careful + eq1.fir_length = 90; % Minimize this vs. fmin/fmax choice + eq1.fir_autoband = 0; % Select manually frequency limits + eq1.fmin_fir = 700; % Equalization starts from 800 Hz + eq1.fmax_fir = 13e3; % Equalization ends at 13 kHz + eq1.fir_minph = 1; % Check result carefully if 1 is used, 0 is safe + eq2 = eq1; % Copy settings to second EQ + + %% Design left channel EQ + eq1.raw_f = f; % Measurement Hz + eq1.raw_m_db = m(:,1); % Measurement dB, left ch + eq1 = eq_compute(eq1); + eq_plot(eq1, 10); + +The run of this script creates these plots. Note the choice of 1.0 +octaves smoothing for both plotting and EQ target derivation. It’s +best to start carefully with such a high amount of smoothing to avoid +to equalize highly uncertain details of frequency response. + +The smoothed version of the response becomes very flat in the +equalized version. However the simulated raw response still contains a +lot of ripple especially at high bands. It’s an industry standard to +use ⅓ octaves smoothing since it quite well matches human ear +psycho-acoustics. Therefore ⅓ octaves should be the smallest feasible +width of octaves smoothing to use. + +.. figure:: Picture_response_with_smoothing.png + :width: 600 + + Imported frequency response with and without octaves + smoothing. Note that the strong 1.0 octaves wide smoothing + “flattens” most of the narrow (high Q) resonances and leaves the + two mentioned resonances at 700 Hz and 4 kHz. + +.. figure:: Picture_FIR_right_channel_equalized.png + :width: 600 + + Simulated frequency response after equalization + +.. figure:: Picture_FIR_response.png + :width: 600 + + Frequency response of equalizer. The blue curve is the ideal + inverse response including the smoothing. The red curve is the band + limited and filter design parameters constrained actual EQ + response. The y-axis is offset in such way that 1 kHz frequency is + shifted to 0 dB. Try the impact of filter length to see how it + impacts the accuracy and find a fair compromise. + +.. figure:: Picture_FIR_response_absolute.png + :width: 600 + + Frequency response of equalizer. This curve shows the absolute gain + of the equalization. It can be seen that the normalization of + loudness (-3 dB) does some fairly high gain above 10 kHz. The + attenuation of frequencies below 200 Hz may or may not be + sufficient to give signal headroom for this boost. Need to watch + out for distortion in playback, if observed the loudness need to be + decreased. + +.. figure:: Picture_FIR_impulse_response.png + :width: 600 + + Impulse response of equalizer. The chosen minimum phase + non-symmetrical impulse response can be seen in the shape. A linear + phase response would have symmetrical pre- and post oscillation in + the impulse response. + +Add of right channel measurement import and EQ design is done by +adding these lines to above script. + + +.. code-block:: octave + + %% Design right channel EQ + eq2.raw_f = f; % Measurement Hz + eq2.raw_m_db = m(:,2); % Measurement dB, right ch + eq2 = eq_compute(eq2); + eq_plot(eq2, 20); + +The resulting EQ can be seen from these plots. If the left and right +channel results are different need to know if it is due to +non-symmetrical mechanics. If there’s designed non-symmetry it’s safe +to go ahead and design different EQ for left and right channels. If +the hardware is symmetrical then it is likely to better to equalize +e.g. average response of left and right instead. + +Note: The left and right responses are quite similar. The mechanics & +acoustics is likely symmetrical so a common EQ could be the best +choice. The average of left and right response could be suitable to +use. However in this in this case the design is done as stereo for +tutorial purpose. + +.. figure:: Picture_right_channel_response.png + :width: 600 + + Import right channel frequency response. + + +.. figure:: Picture_FIR_right_channel_equalized.png + :width: 600 + + Simulated response of equalizer. + +.. figure:: Picture_right_channel_FIR_absolute_response.png + :width: 600 + + Frequency response of the right channel filter. Notice the difference to left channel filter. + +The next step is to check the stereo EQ design. The left and right +channels should as equalized have similar loudness. Since the SOF tool +currently does not add much help to multi-channel design this step +needs some additional own code. + +.. code-block:: octave + + %% Stereo EQ + figure(30); + l_ch = eq1.m_db+eq1.fir_eq_db; + r_ch = eq2.m_db+eq2.fir_eq_db; + semilogx(eq1.f, l_ch, eq2.f, r_ch); + grid on; + axis([100 20e3 -20 10]); + xlabel('Frequency (Hz)'); + ylabel('Magnitude (dB)'); + + %% Calculate level offset at 1 - 4 kHz from RMS + idx0 = find(eq1.f < 4e3); + idx = find(eq1.f(idx0) > 1e3); + l_lev = 20*log10(sqrt(mean(10.^(l_ch(idx)/10)))); + r_lev = 20*log10(sqrt(mean(10.^(r_ch(idx)/10)))); + fprintf('L ch level %3.1f dB\n', l_lev); + fprintf('R ch level %3.1f dB\n', r_lev); + delta_lev = l_lev-r_lev; + fprintf('delta %3.1f dB\n', delta_lev); + +The plot shows the raw data plus EQ impact. Since the offset is hard +to judge from the non-smoothed plot (the smoothed data is +unfortunately for this purpose 1 kHz, 0 dB aligned) the offset is +computed from RMS level difference in 1 - 4 kHz band. In this example +the difference was 0.2 dB. The offset is next added to right channel +align. + +.. code-block:: octave + + %% Design right channel EQ + eq2.norm_offs_db = -3 + 0.2; % Offset in dB to normalize, -3dB plus L-R + eq2.raw_f = f; % Measurement Hz + eq2.raw_m_db = m(:,2); % Measurement dB, right ch + eq2 = eq_compute(eq2); + eq_plot(eq2, 20); + + +.. figure:: Picture_simulated_left_and_right_channel_responses.png + :width: 600 + + Simulated frequency responses of left and right speaker channels. + +The complete tuning script is shown below for completeness. It can be a +starting point for your own stereo speaker equalizer design case! + + +.. code-block:: octave + + %% Load measurement data, variable f and m + load example_dut.mat; + + %% EQ settings + eq1 = eq_defaults(); % Get defaults + eq1.fs = 48e3; % Set sample rate + eq1.norm_type = 'loudness'; % Normalize criteria can be loudness/peak/1k + eq1.norm_offs_db = -3; % Offset in dB to normalize, -3dB loudness + eq1.logsmooth_plot = 1.0; % Smooth over 1.0 octaves + eq1.logsmooth_eq = 1.0; % Smooth over 1.0 octaves + eq1.enable_fir = 1; % By default both FIR and IIR disabled + eq1.fir_beta = 3.0; % Lower beta is more accurate but be careful + eq1.fir_length = 90; % Minimize this vs. fmin/fmax choice + eq1.fir_autoband = 0; % Select manually frequency limits + eq1.fmin_fir = 700; % Equalization starts from 800 Hz + eq1.fmax_fir = 13e3; % Equalization ends at 20 kHz + eq1.fir_minph = 1; % Check result carefully if 1 is used, 0 is safe + eq2 = eq1; % Copy settings to second EQ + + %% Design left channel EQ + eq1.raw_f = f; % Measurement Hz + eq1.raw_m_db = m(:,1); % Measurement dB, left ch + eq1 = eq_compute(eq1); + eq_plot(eq1, 10); + + %% Design right channel EQ + eq2.norm_offs_db = -3 + 0.2; % Offset in dB to normalize, -3dB plus L-R + eq2.raw_f = f; % Measurement Hz + eq2.raw_m_db = m(:,2); % Measurement dB, right ch + eq2 = eq_compute(eq2); + eq_plot(eq2, 20); + + %% Stereo EQ + figure(30); + l_ch = eq1.m_db+eq1.fir_eq_db; + r_ch = eq2.m_db+eq2.fir_eq_db; + semilogx(eq1.f, l_ch, eq2.f, r_ch); + grid on; + axis([100 20e3 -20 10]); + xlabel('Frequency (Hz)'); + ylabel('Magnitude (dB)'); + + %% Calculate level offset at 1 - 4 kHz from RMS + idx0 = find(eq1.f < 4e3); + idx = find(eq1.f(idx0) > 1e3); + l_lev = 20*log10(sqrt(mean(10.^(l_ch(idx)/10)))); + r_lev = 20*log10(sqrt(mean(10.^(r_ch(idx)/10)))); + fprintf('L ch level %3.1f dB\n', l_lev); + fprintf('R ch level %3.1f dB\n', r_lev); + delta_lev = l_lev-r_lev; + fprintf('delta %3.1f dB\n', delta_lev); + +IIR equalizer +************* + +Infinite impulse response (IIR) filter is the other main filter type +for equalization. Here it’s described after FIR because despite the +simpler look (much lower filter orders needed) using them needs more +expertise. An IIR design can fail fatally if not used with care and +plenty of testing. Therefore it is recommended to use simple low order +filters and do the more complex response manipulation with FIR. The +risks of IIR are in stability (unwanted loud oscillation), noise, and +loss of SNR due to scaling need. However IIR filters are great for +enhancing frequency response at lowest frequencies and generally doing +stronger adjustment. + +The tool in SOF does not support automatic design. Instead the design +is manual with parametric first and second order blocks. The second +order blocks are called often bi-quads. The parametric blocks are +specified by their type (high-pass, low-pass, low-shelf, high-shelf, +peak/notch). The shelving and peaking filters are second order. The +high-pass and low-pass filters can be first or second order. Therefore +the parametric blocks are called with abbreviations HP1, HP2, LP1, +LP2, LS2, HS2, and PN2. All parametric blocks have a resonant +frequency parameter in Hz. The shelving filters and peaking filters +have also gain in Decibels as parameter. Finally the peaking filter +has a Q-value parameter. The higher the Q-value is the narrower is the +resonance. The syntax for describing parametric EQ is shown below: + +.. code-block:: octave + + eq1.peq = [ eq1.PEQ_HP2 200 0 0 ; ... + eq1.PEQ_PN2 750 -5.0 1.3 ; ... + eq1.PEQ_PN2 5000 -4.0 0.6 ; ... + ]; + + +The example can be equalized with IIR only. First, since there is very +little output from the speaker below 200 Hz we can with second order +high-pass suppress the not audible frequencies from output. It +increases the headroom for equalization a lot since typical music and +speech content has large energy there. Then, a peaking EQ is set to +attenuate the 750 Hz region by 5 dB and Q-value 1.3 for flatter +response. Finally, a peaking filter is set to attenuate the wide bump +at 5 kHz by 4 dB and Q-value 0.6. The resulting EQ is 6th order. It +also could be possible to boost the low frequencies at 400 Hz a bit +with a low-shelf but it is not done here to keep filter order +low. Boost at low frequencies creates risk for signal clipping while +the achievable bandwidth extension is not large. + +.. figure:: Picture_imported_frequency_response_for_iir.png + :width: 600 + + Simulated frequency response. The difference in parametric + low-order IIR can be seen as more remaining small ripple in the + smoothed equalized response vs. FIR. + +.. figure:: Picture_iir_filter_response_vs_ideal_target.png + :width: 600 + + IIR filter response vs. ideal target. + +.. figure:: Picture_iir_absolute_response.png + :width: 600 + + Absolute response. The loudness normalize suggests a fairly high + gain for the filter since a lot of loudness is lost due to suppress + of lowest frequencies. Need to be careful with this. + +.. figure:: Picture_iir_poles_and_zeros.png + :width: 600 + + Poles and zeros plot. In recursive filters the poles (x) need to be + inside unit circle for stable design. This plot is for 64 bit float + coefficients, fixed scaled coefficients could have issues even if + this looks OK. + +.. figure:: Picture_iir_impulse_response.png + :width: 600 + + Impulse response. The main purpose of this to do another stability + check. A stable filter decays to zero while an unstable design + might remain oscillation at steady or increasing amplitude. + +The right channel is tuned similarly. The resulting non-smoothed +left/right balance corrected responses and the complete code for +tuning are shown below. + + +.. figure:: Picture_iir_simulated_left_and_channel_responses.png + :width: 600 + + Simulated frequency responses of left and right speakers with + IIR equalizer. + + +.. code-block:: octave + + %% Load measurement data, variable f and m + load example_dut.mat; + + %% EQ settings + eq1 = eq_defaults(); % Get defaults + eq1.fs = 48e3; % Set sample rate + eq1.norm_type = 'loudness'; % Normalize criteria can be loudness/peak/1k + eq1.norm_offs_db = -3; % Offset in dB to normalize, -3 dB loudness + eq1.logsmooth_plot = 1.0; % Smooth over 1.0 octaves + eq1.logsmooth_eq = 1.0; % Smooth over 1.0 octaves + eq1.enable_iir = 1; % By default both FIR and IIR disabled + eq2 = eq1; % Copy settings to second EQ + + %% Design left channel EQ + eq1.raw_f = f; % Measurement Hz + eq1.raw_m_db = m(:,1); % Measurement dB, left ch + eq1.peq = [ eq1.PEQ_HP2 200 0 0 ; ... + eq1.PEQ_PN2 750 -5.0 1.3 ; ... + eq1.PEQ_PN2 5000 -4.0 0.6 ; ... + ]; + eq1 = eq_compute(eq1); + eq_plot(eq1, 10); + + %% Design right channel EQ + eq2.norm_offs_db = -3 + 0.1; % Offset in dB to normalize, -3dB plus L-R + eq2.raw_f = f; % Measurement Hz + eq2.raw_m_db = m(:,2); % Measurement dB, right ch + eq2.peq = [ eq2.PEQ_HP2 200 0 0 ; ... + eq2.PEQ_PN2 750 -5.0 1.4 ; ... + eq2.PEQ_PN2 4500 -4.0 0.6 ; ... + ]; + eq2 = eq_compute(eq2); + eq_plot(eq2, 20); + + %% Stereo EQ + figure(30); + l_ch = eq1.m_db+eq1.iir_eq_db; + r_ch = eq2.m_db+eq2.iir_eq_db; + semilogx(eq1.f, l_ch, eq2.f, r_ch); + grid on; + axis([100 20e3 -20 20]); + xlabel('Frequency (Hz)'); + ylabel('Magnitude (dB)'); + + %% Calculate level offset at 1 - 4 kHz from RMS + idx0 = find(eq1.f < 4e3); + idx = find(eq1.f(idx0) > 1e3); + l_lev = 20*log10(sqrt(mean(10.^(l_ch(idx)/10)))); + r_lev = 20*log10(sqrt(mean(10.^(r_ch(idx)/10)))); + fprintf('L ch level %3.1f dB\n', l_lev); + fprintf('R ch level %3.1f dB\n', r_lev); + delta_lev = l_lev-r_lev; + fprintf('delta %3.1f dB\n', delta_lev); + +Combined IIR and FIR +******************** + +The EQ tool can support use of both types simultaneously. The IIR type +is applied first and the impact is subtracted from the target. This +allows the FIR to fine tune the response where IIR could not match +fully the target. + +For this example the IIR high shelf is left out because FIR can do it +efficiently. Instead of boosting at 2 kHz this script tests +attenuation at 700 Hz to flatten and extend a bit the flat frequency +response region down. + +Note: In current version the norm_offs_db parameter impacts both FIR +and IIR part by the given amount. Therefore the level adjust need to +be entered as 0.5*adjust. + +.. figure:: Picture_IIR_FIR_target_vs_achieved_response.png + :width: 600 + + Right channel equalization filters. The red solid plot is the combined IIR and FIR response + that matches well the smoothed target response in solid blue. The dashed yellow and purple + lines show the IIR and FIR responses. + +.. figure:: Picture_simulated_IIR_FIR_frequency_response.png + :width: 600 + + Simulated raw frequency response + +Exporting coefficients to SOF +***************************** + +The coefficients can be exported into a format for m4 topology for +automatic boot time setup. The topology file can include the m4 +scripts instead of the default “flat” response coefficients. It is +also possible to set up an equalizer with .txt or .bin format blob in +device run-time with sof-ctl utility to test the response and iterate +the design. + +The complete script for equalizers tuning and coefficients export for +the previous example is shown below. + +.. code-block:: octave + + %% Load measurement data, variable f and m + load example_dut.mat; + + %% EQ settings + eq1 = eq_defaults(); % Get defaults + eq1.fs = 48e3; % Set sample rate + eq1.norm_type = 'loudness'; % Normalize criteria can be loudness/peak/1k + eq1.norm_offs_db = -3; % Offset in dB to normalize, -3dB loudness + eq1.logsmooth_plot = 1.0; % Smooth over 1.0 octaves + eq1.logsmooth_eq = 1.0; % Smooth over 1.0 octaves + eq1.enable_fir = 1; % By default both FIR and IIR disabled + eq1.enable_iir = 1; % Enable too + eq1.fir_beta = 3.0; % Lower beta is more accurate but be careful + eq1.fir_length = 40; % Minimize this vs. fmin/fmax choice + eq1.fir_autoband = 0; % Select manually frequency limits + eq1.fmin_fir = 700; % Equalization starts from 800 Hz + eq1.fmax_fir = 13e3; % Equalization ends at 13 kHz + eq1.fir_minph = 1; % Check result carefully if 1 is used, 0 is safe + eq2 = eq1; % Copy settings to second EQ + + %% Design left channel EQ + eq1.raw_f = f; % Measurement Hz + eq1.raw_m_db = m(:,1); % Measurement dB, left ch + eq1.peq = [ eq1.PEQ_HP2 200 0 0 ; ... + eq1.PEQ_PN2 750 -5.0 1.3 ; ... + ]; + eq1 = eq_compute(eq1); + eq_plot(eq1, 10); + + %% Design right channel EQ + eq2.norm_offs_db = -3 + 0.1; % Offset in dB to normalize, -4dB plus L-R + eq2.raw_f = f; % Measurement Hz + eq2.raw_m_db = m(:,2); % Measurement dB, right ch + eq2.peq = [ eq2.PEQ_HP2 200 0 0 ; ... + eq2.PEQ_PN2 750 -5.0 1.4 ; ... + ]; + eq2 = eq_compute(eq2); + eq_plot(eq2, 20); + + %% Stereo EQ + figure(30); + l_ch = eq1.m_db+eq1.tot_eq_db; + r_ch = eq2.m_db+eq2.tot_eq_db; + semilogx(eq1.f, l_ch, eq2.f, r_ch); + grid on; + axis([100 20e3 -20 10]); + xlabel('Frequency (Hz)'); + ylabel('Magnitude (dB)'); + + %% Calculate level offset at 1 - 4 kHz from RMS + idx0 = find(eq1.f < 4e3); + idx = find(eq1.f(idx0) > 1e3); + l_lev = 20*log10(sqrt(mean(10.^(l_ch(idx)/10)))); + r_lev = 20*log10(sqrt(mean(10.^(r_ch(idx)/10)))); + fprintf('L ch level %3.1f dB\n', l_lev); + fprintf('R ch level %3.1f dB\n', r_lev); + delta_lev = l_lev-r_lev; + fprintf('delta %3.1f dB\n', delta_lev); + + %% Export FIR + fir_ascii_fn = 'dut_spk_fir.txt'; + fir_tplg_fn = 'dut_spk_fir.m4'; + fir_eq1_quant = eq_fir_blob_quant(eq1.b_fir); + fir_eq2_quant = eq_fir_blob_quant(eq2.b_fir); + channels_in_config = 2; % Setup max 2 channels EQ + assign_response = [0 1]; % Switch to response #0 and #1 + num_responses = 2; % Two responses + fir_bm = eq_fir_blob_merge(channels_in_config, ... + num_responses, ... + assign_response, ... + [fir_eq1_quant fir_eq2_quant]); + fir_bp = eq_fir_blob_pack(fir_bm); + eq_alsactl_write(fir_ascii_fn, fir_bp); + eq_tplg_write(fir_tplg_fn, fir_bp, 'FIR'); + + %% Export IIR + iir_ascii_fn = 'dut_spk_iir.txt'; + iir_tplg_fn = 'dut_spk_iir.m4'; + iir_eq1_quant = eq_iir_blob_quant(eq1.p_z, eq1.p_p, eq1.p_k); + iir_eq2_quant = eq_iir_blob_quant(eq2.p_z, eq2.p_p, eq2.p_k); + iir_bm = eq_iir_blob_merge(channels_in_config, ... + num_responses, ... + assign_response, ... + [iir_eq1_quant iir_eq2_quant]); + iir_bp = eq_iir_blob_pack(iir_bm); + eq_alsactl_write(iir_ascii_fn, iir_bp); + eq_tplg_write(iir_tplg_fn, iir_bp, 'IIR'); + +Testing the response with sof-ctl +********************************* + +The sof-ctl tool is practical for testing new EQ settings and iterate +the design without need to reboot the device. The pre-requisite is that +the DUT runs for speaker path a topology that contains the IIR and FIR +equalizers. + +First the numids of the equalizers are found out with amixer +command. The lines with prompt $ are user entered commands and other +text shown is command output. + +.. code-block:: bash + + $ amixer -Dhw:0 controls | grep EQIIR + numid=66,iface=MIXER,name='EQIIR1.0 EQIIR' + + $ amixer -Dhw:0 controls | grep EQFIR + numid=67,iface=MIXER,name='EQFIR1.0 EQFIR' + +The numids are in this device 66 and 67 for IIR and FIR. Next the +exported ALSA binary controls are passed to equalizers with sof-ctl: + +.. code-block:: bash + + $ ./sof-eqctl -n 66 -s dut_spk_iir.txt + Applying configuration "dut_spk_iir.txt" into device hw:0 control numid=66. + + 4607827,0,196,50331648,0,0,0,0,196,2,2,0,0,0,0,0,1,2,2,0,0,0,0,3260252783,2107733822, + 528275171,3238416955,528275171,0,16384,3324016838,2034846530,497901563,3275128193, + 526872106,4294967293,20454,2,2,0,0,0,0,3260252783,2107733822,528275171,3238416955, + 528275171,0,16384,3317002057,2041827532,500647939,3271629404,527641448,4294967293,20551 + + Success. + + $ ./sof-eqctl -n 67 -s dut_spk_fir.txt + Applying configuration "dut_spk_fir.txt" into device hw:0 control numid=67. + + 4607827,0,244,50331648,0,0,0,0,244,131074,0,0,0,0,65536,44,0,0,0,0,3801503801,233243489, + 4293068324,74908123,1901269,7733144,6422742,4290772934,17039467,1114313,4293328827, + 4291756033,4289658785,4291297224,4293459912,589833,4294115318,4294246391,4294442989, + 1310731,13,0,44,0,0,0,0,3785054386,221118972,13436579,74515002,8520459,10551247,10944817, + 4292018112,23789790,4291559609,4293984167,4288479207,4290576265,4293394406,131047,1179673, + 4293853177,4293853167,4294901744,851980,6,0 + + Success. + + + +.. figure:: Picture_tested_speaker_frequency_response.png + :width: 600 + + The response is simple to test acoustically by re-running + mls_freq_resp(); The overall response is now much more flat and is + very similar to previously shown simulated response. + + +Using the EQ settings in topology +********************************* + +The generated .m4 suffix files for FIR and IIR can be included or +embedded into topology m4 scripts. There are a few examples of such +topologies in $SOF_WORKSPACE/sof/tools/topology/topology1/development. +The CMakeLists.txt file builds e.g. topologies +sof-cml-rt1011-rt5682-eq.tplg and sof-hda-generic-2ch-loud.tplg those +can be used as example. + +The playback pipeline is set with -DSPKPROC=eq-iir-eq-fir-volume +or -DHSPROC=eq-iir-eq-fir-volume to contain the equalizers and volume +control components. The macros -DHSPROC_FILTER1=eq_iir_coef_pass.m4 +and -DHSPROC_FILTER2=eq_fir_coef_pass.m4 are flat default responses. + +Setting -DHSPROC_FILTER1=dut_spk_iir.m4 and +-DHSPROC_FILTER2=dut_spk_fir.m4 would set the just exported equalizer +tuning to be applied at device boot. + +Note: Unfortunately the SOF topology1 equalizers definitions at top +CMakeLists.txt are not very systematic and there may be bugs with some +platforms triggered by small topology changes. The new topology needs +extensive testing for all audio endpoints (that other existing filters +are not modified) and preferably manual inspection of topology .conf +file that the m4 parsed output matches expectation. + +The development now focuses to to topology2 and hopefully this part +can be cleaned up and made easier for product audio tuning. + +References +********** + +.. [1] AES17-2020: AES standard method for digital audio engineering - Measurement of digital audio equipment, + https://www.aes.org/publications/standards/search.cfm?docID=21 + +.. [2] Dayton audio UMM-6 USB measurement microphone, + https://www.daytonaudio.com/product/1116/umm-6-usb-measurement-microphone + +.. [3] MiniDSP UMIK-1 USB measurement microphone, + https://www.minidsp.com/products/acoustic-measurement/umik-1 diff --git a/algos/index.rst b/algos/index.rst index 34776ba9..6cd9fb9c 100644 --- a/algos/index.rst +++ b/algos/index.rst @@ -37,6 +37,7 @@ Further information on specific algorithms is forthcoming. .. toctree:: :maxdepth: 1 - src/sample_rate_conversion demux/demux.rst + eq/equalizers_tuning + src/sample_rate_conversion tdfb/time_domain_fixed_beamformer