Matlab: Apply a LPF in the time and frequency using filter() and freqz()

The code below shows how to implement a 1000Hz Butterworth low pass filter using the filter() function in time domain and freqz() function in the complex frequency domain.

>> load mtlb %Load the 'Matlab' speech / dimention: 4001x1
>> sound(mtlb,Fs); %Play the original sound
>> len = length(mtlb); %Number of points
>> time = [1:len]/Fs; %x-axis time vector / dimention: 1x4001
>> subplot(3,1,1);
>> plot(time,mtlb);
>> title('Original Speech');

>> [b, a] = butter(3,1000/(Fs/2),'low'); %design a Butterworth filter

Time domain
>> y1 = filter(b, a, mtlb); %get time domain result directly % dimention: 4001x1
>> sound(y1,Fs); %Play the sound processed by filter()
>> subplot(3,1,2);
>> plot(time,y1);
>> title('filter()');

Frequency domain (Method 1)
>> mtlb_FFT = fft(mtlb); %transformed input signal / dimention: 4001x1
>> H = freqz(b, a, len, 'whole'); %filter transfer function / dimention: 4001x1
>> Y2_FFT = mtlb_FFT .* H; %filtered result in freq. domain = multiplication of transformed speech signal and the filter transfer function in the freq. domain. % dimention: 4001x1
>> y2 = ifft(Y2_FFT); %Inverse FFT to time domain % dimention: 4001x1
>> sound(y2, Fs);
>> subplot(3,1,3);
>> plot(time,y2);
>> title('freqz() and transform');

Frequency domain (Method 2)
>> mtlb_FFT = fft(mtlb); %transformed input signal / dimention: 4001x1
>> H = freqz(b, a, len); %filter transfer function / dimention: 4001x1
>> Y2_FFT = mtlb_FFT .* H; %filtered result in freq. domain = multiplication of transformed speech signal and the filter transfer function in the freq. domain. % dimention: 4001x1
>> y2 = ifft(Y2_FFT); %Inverse FFT to time domain % dimention: 4001x1
>> sound(abs(y2), Fs);
>> subplot(3,1,3);
>> plot(time,y2);
>> title('freqz() and transform');

Result:

References:

Matlab: Low pass filtered Chirp sound - Study EECC
Filter Applications (濾波器應用) - Audio Signal Processing and Recognition (音訊處理與辨識)
MATLAB: filter in the frequency domain using FFT/IFFT with an IIR filter - StackOverflow