Arbitrary response Filterbuilder Amplitude question

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.

Answer 1

[Wayne King]

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.

Answer 2

[Wayne King]

Are these power measurements in dB?

In other words are these A^2 measurements where A is the desired amplitude?

In that case, you can just use:

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));

But the first element of your frequency vector must be 0 and the last element must be the Nyquist.

I'll just repeat the value for 12.5 in my example:

 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];
 d = fdesign.arbmag('N,F,A',200,F,A,48000);
 Hd = design(d);

[tony karamp]

Hello Wayne and thank you for taking the time to answer me. The measurements are in dB Sound Pressure Level (dB SPL). The two vectors were created in Easera software and I took the info for the frequency and the SPL. I read somewhere that I have to convert the dB SPL vector into amplitude (so I just use 20*log10(dB)?) and then insert that vector to the Amplitude slot of the filter. As for the frequency, I don't believe it has to start from zero, rather just monotonically increase.

Thank you!