----------Added at 2019/9/2 22:36;
An important but missing information seems to be the order of my filter. I designed my filter with numerator and denominator length both equal to 20, so the order is 38. Specific coefficients are shown in the following image:filter coefficients.
----------Added at 2019/9/2 18:42; 1st updated at 9/2 22:51;
According to @Irreducible, I add the magnitude of the unfiltered signal and the filtered signal as follow. As it was figured in 'filtering result' image, the magnitude of unfiltered signal kept at a level of less than 0.1 and got an mean value of 1.9337e-07, while the magnitude of the filtered signal seemed to be amplified to 'Nan' level by simply having a glance of mean(filt) or mean(filt_sos) and got 'NaN' as result.
For more information, see 'filt' data filt data, or the magnitude comparison among 'unfiltered raw signal','filtered signal using filter()' and 'filtered signal using sosfilt()' unfiltered, filt, filt_sos.
Using dB scale and cut off y-axis, plot the magnitude of unfiltered and filtered signal again dB-scale and truncated-y-axis filtered signal. As shown in the image, from certain time on, the magnitude would keep at 'NaN' level.
But according to magnitude response of the filter, it should amplify the raw data with no more than 30 dB. So I thought there must be something wrong here.
1. Problem description
I'm trying to filter data with an IIR filter, with using Y=filter(b,a,X) in MATLAB. I've got the numerator and denominator coefficients, and with freqz(b,a) I'm sure this is the filter I need. However, after I do filter(b,a,sig), the output seemed to be beyond my expectation. I've worked on it a few days with no progress.
Anyone may help me out here? What's wrong with my code, or what's the exactly right way to use numerator and denominator coefficients to filter data?
2. Main code
Here is my code, for brevity, I omit some coefs:
clear;close all;clc;
%%% load data
[wav,Fs]= audioread('G:\Program\MATLAB\wavEQ\Experiment\raw.wav');
sig = wav(:,1); % data to be filtered
%%% get numerator and denominator coefficients
allCoef = [9.022012513759181 0.48509530946330026 ...];
len_b = ceil(length(allCoef)/2);
b = allCoef(1:len_b);
a(1) = 1;
a(2:length(allCoef)-len_b+1)= allCoef(len_b+1:length(allCoef));
%%% filtering
filt = filter(b, a, sig); % IIR filtering
%%% sos-type filtering
[SOS,~] = tf2sos(b,a);
filt_sos = sosfilt(SOS, sig);
%%% figure
figure;
subplot(311)
plot(sig);title('orgin signal');
subplot(312)
plot(filt);title('filt');
subplot(313)
plot(filt_sos);title('filt_sos');
% wav_filtering = [sig1_filtering,wav(:,2)];
% audiowrite('raw_FIR_filtering.wav', wav_filtering, Fs);
3. Filtering result
With freqz(b,a) or fvtool(b,a), I'm pretty sure this is the mag-response I need:
magnitude response
The filtering result was as follow: filtering result
The filtering signal's amplitude was much higher than the origin signal's, which was quite not consistent with the mag-response evidently.
By the way, the frequency of the origin signal is between 0 and 10000 Hz, the sampling rate of raw data is 51200 Hz, and the sampling frequency of my IIR filter is 51200 Hz.
4. My consideration
Firstly, I thought there must be something wrong with my usage of filter(b,a,X), then I help filter and learn that "The filter is a 'Direct Form II Transposed' implementation of the standard difference equation:". I tried to convert coefficients to SOS type with [sos,~]=tf2sos(b,a), but the filtering result was still far from expectation (using sosfilt(sos)).
I couldn't help believing that I may have trouble with understanding the relationship between transfer function and coefficients of the filters. But what happened with filter(b,a,X) since I could get ideal frequency response using these b & a with freqz(b,a). Are b and a in these two functions represent different things? Any suggestion would be great appreciated.