How to use a designed filter to convolve a signal.

I designed a filter using the filter designer but I don't know how to use the exported code. I want to use the coefficients produced from the filter to convolve the signal and the filter together (without exporting and loading the coefficients).

Sample Designed filter:

function Hd = lowpassfilter_0_10
%LOWPASSFILTER_0_10 Returns a discrete-time filter object.

% MATLAB Code
% Generated by MATLAB(R) 9.1 and the DSP System Toolbox 9.3.
% Generated on: 24-Apr-2017 10:42:14

% Equiripple Lowpass filter designed using the FIRPM function.

% All frequency values are in Hz.
Fs = 204;  % Sampling Frequency

Fpass = 0;               % Passband Frequency
Fstop = 10;              % Stopband Frequency
Dpass = 0.057501127785;  % Passband Ripple
Dstop = 0.0001;          % Stopband Attenuation
dens  = 20;              % Density Factor

% Calculate the order from the parameters using FIRPMORD.
[N, Fo, Ao, W] = firpmord([Fpass, Fstop]/(Fs/2), [1 0], [Dpass, Dstop]);

% Calculate the coefficients using the FIRPM function.
b  = firpm(N, Fo, Ao, W, {dens});
Hd = dfilt.dffir(b);

How do I use this function within a code to convolve a signal and this filter together? Do I have to do something like:

filtered_signal = conv(signal, Hd);

*To explain the process further: Right now I'm just designing the filter in filter designer, exporting the coefficients into an .mat file, and getting the filtered signal using the convolution.

signal = C{1,1}{1,2}; %my data is in C{1,1}{1,2}
uiopen('matlab','Select filter'); %getting the exported coefficients (variable name lowpass)
fsignal = conv(signal,lowpass); %convolving the signal and filter

Is there a better way to do this without exporting and importing into the workspace and just using the exported code above?

Answer 1

[Honglei Chen]

You may want to use

filtered_signal = filter(Hd,signal);

filter and conv is essentially the same except that filter keeps the output the same size as input and save extra samples in the state for the signal in the next frame. If you really want to use conv you can do

filtered_signal = conv(signal, Hd.Numerator);

HTH

[Jason Jeong]

I used

filtered_signal = filter(function_name,signal);

and that seemed to work. Thank you!

There is a small annoyance though, it seems like the filtered signal is shifted to the right a bit than the original signal. If my understanding of convolutions is correct, then it adds 30-some samples to each side of the output and that might be the reason for the shift. But does filter do the same thing or does it cut out the "outsides"?

Example: If I have the original data as 1024x1, and I convolve it with a filter I get a filtered data set of something like 1056x1. With the filter function can I assume that it deletes the first 16 and last 16 points to get 1024x1?

[Honglei Chen]

That sounds odd, filter should just match the first 1024 samples, at least for the first call. Could you elaborate the delay you see? Below is a quick test I did on my side

>> H = dfilt.dffir(rand(1,5))

H =

       FilterStructure: 'Direct-Form FIR'                                                                            
            Arithmetic: 'double'                                                                                     
             Numerator: [0.277438718955492 0.00610780302659897 0.374711141145558 0.436932780731988 0.304298468841678]
      PersistentMemory: false                                                                                        

>> filter(H,ones(1,10))

ans =

      0.2774    0.2835    0.6583    1.0952    1.3995    1.3995    1.3995    1.3995    1.3995    1.3995

>> conv(H.Numerator,ones(1,10))

ans =

    Columns 1 through 11

      0.2774    0.2835    0.6583    1.0952    1.3995    1.3995    1.3995    1.3995    1.3995    1.3995    1.1221

    Columns 12 through 14

      1.1159    0.7412    0.3043

[Jason Jeong]

This is the weird image I get. You can pretty easily see that the filtered signal looks shifted to the right.

As for the quick test, this is what I got:

>> H = dfilt.dffir(rand(1,5))

H =

       FilterStructure: 'Direct-Form FIR'                                                                           
            Arithmetic: 'double'                                                                                    
             Numerator: [0.0975404049994095 0.278498218867048 0.546881519204984 0.957506835434298 0.964888535199277]
      PersistentMemory: false        

>> filter(H,ones(1,10))

ans =

      0.0975    0.3760    0.9229    1.8804    2.8453    2.8453    2.8453    2.8453    2.8453    2.8453

>> conv(H.Numerator,ones(1,10))

ans =

    Columns 1 through 11

      0.0975    0.3760    0.9229    1.8804    2.8453    2.8453    2.8453    2.8453    2.8453    2.8453    2.7478

    Columns 12 through 14

      2.4693    1.9224    0.9649

I did some further looking into it, just trying the convolution (gave me 1075x1) and plotting. I see that the convolution (blue) is the same as the filtered one (red) so it seems like the filtering just cuts off the last 51 data points to get the filtered signal (1024x1) without centering it.

[Honglei Chen]

Yes, that is correct. I think I now understand what you mean by the delay. That is not the difference between filter and conv command. Rather it is the group delay introduced by the filtering operation itself.

HTH