MATLAB: Arbitrary response Filterbuilder Amplitude question

amplitudearbitrarydbfilterfilterbuilderfrequencyspl

Hello all,
currently I am trying to create an Arbitrary Response filter using filterbuilder. So I open filterbuilder, select the Arbitrary Response Filter. In the Main tab I set Impulse Response to FIR, Order of 200 and Filter Type Single-rate. In the Response Specifications the number of bands is 1, I have specified the response as Amplitudes and the Frequency units are set to Hz. I set the Input Fs equal to 48000Hz. As far as frequency is concerned, I have a vector with values
 freq = [12.500  16.000  20.000  25.000  31.500  40.000  50.000  63.000...
    80.000  100.000  125.000  160.000  200.000  250.000  315.000  400.000...
    500.000  630.000  800.000  1000.00  1250.00  1600.00  2000.00  2500.00...
    3150.00  4000.00  5000.00  6300.00  8000.00  10000.0  12500.0  16000.0  20000.0];
I also have the corresponding dB SPL vector
 dB = [108.8  104.5  111.4  116.2  116.5  114.7  122.4  130.8...
    127.2  133.4  129.6  137.2  136.0  137.5  136.6  136.2...
    134.0  135.0  133.7  133.8  133.1  132.6  131.8  131.9...
    132.3  131.2  131.6  131.6  132.9  131.4  127.6  124.1  125.2];
Now, back in filterbuilder I use the freq vector as the Frequencies input. What should I be using for the Amplitude input? I know that I can't use the dB SPL vector as is.
Thank you all very much in advance.

Best Answer

Tony, You're incorrect about the frequency vector, it must begin at 0 and end with Fs/2
I've shown you already how to convert dB SPL to amplitudes:
dB = [108.8 108.8 104.5  111.4  116.2  116.5  114.7  122.4  130.8...
127.2  133.4  129.6  137.2  136.0  137.5  136.6  136.2...
134.0  135.0  133.7  133.8  133.1  132.6  131.8  131.9...
132.3  131.2  131.6  131.6  132.9  131.4  127.6  124.1  125.2];
A = sqrt(db2pow(dB));
A is now your amplitude vector. Note that I simply repeated the entry for 12.5 Hz for the necessary 0 frequency value.
Now for your frequency vector, it must begin with 0 and end with Fs/2.
F  = [0 12.500  16.000  20.000  25.000  31.500  40.000  50.000  63.000...
  80.000  100.000  125.000  160.000  200.000  250.000  315.000  400.000...
  500.000  630.000  800.000  1000.00  1250.00  1600.00  2000.00  2500.00...
  3150.00  4000.00  5000.00  6300.00  8000.00  10000.0  12500.0  16000.0  24000.0];
You can paste the F and the A vector into the Workspace and then put those variables F and A in the Arbitrary Response Design dialog, or simply use the code I gave you in my first answer which does exactly what filterbuilder does from the command line.
Thank you for accepting my answer if I have helped you.
If you want you can try to have a first frequency element not equal to 0 and a last element not equal to Fs/2, but it will errror.
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