How do I define parameters in a convolution equation? - matlab

Question

I am trying to compute the convolution of a sound signal without using the built in conv function but instead using arrays. x is the input signal and h is are the impulse responses. However, when I run my other main function to call onto my_conv I am getting these errors:
Undefined function or variable 'nx'.**
Error in my_conv (line 6)
ly=nx+nh-1;
Error in main_stereo (line 66)
leftchannel = my_conv(leftimp, mono); % convolution of left ear impulse response and mono
This is my function my_conv:
function [y]=my_conv(x,h)
x=x(:);
h=h(:);
lx=length(x);
lh=length(h);
ly=nx+nh-1;
Y=zeros(nh,ny);
for i =1:nh
Y((1:nx)+(i-1),i)=x;
end
y=Y*h;
What changes should I make to fix these errors and get this code running?
I am trying to immplement the function into this code:
input_filename = 'speech.wav';
stereo_filename = 'stereo2.wav';
imp_filename = 'H0e090a.dat';
len_imp = 128;
fp = fopen(imp_filename, 'r', 'ieee-be');
data = fread(fp, 2*len_imp, 'short');
fclose(fp);
[mono,Fs] = audioread(input_filename);
if (Fs~=44100)
end
len_mono = length(mono);
leftimp = data(1:2:2*len_imp);
rightimp = data(2:2:2*len_imp);
leftchannel = my_conv(leftimp, mono);
rightchannel = my_conv(rightimp, mono);
leftchannel = reshape(leftchannel , length(leftchannel ), 1);
rightchannel = reshape(rightchannel, length(rightchannel), 1);
norml = max(abs([leftchannel; rightchannel]))*1.05;
audiowrite(stereo_filename, [leftchannel rightchannel]/norml, Fs);

Answer 1

As pointed out by #SardarUsama in comments, the error
Undefined function or variable 'nx'.
Error in my_conv (line 6) ly=nx+nh-1;
tells you that the variable nx has not been defined before before its usage on the line ly=nx+nh-1. Given the naming of the variables and their usage, it looks like what you intended to do was:
nx = length(x);
nh = length(h);
ny = nx+nh-1;
After making these modifications and solving the first error, you are likely going to get another error telling you that
error: my_conv: operator *: nonconformant arguments
This error is due to an inversion in the specified size of the Y matrix. This can be fixed by initializing Y with Y = zeros(ny, nh);. The resulting my_conv function follows:
function [y]=my_conv(x,h)
nx=length(x);
nh=length(h);
ny=nx+nh-1;
Y=zeros(ny,nh);
for i =1:nh
Y((1:nx)+(i-1),i)=x;
end
y=Y*h;
Note that storing every possible shifts of one of the input vectors in the matrix Y to compute the convolution as a matrix multiplication is not very memory efficient (requiring O(NM) storage). A more memory efficient implementation would compute each element of the output vector directly:
function [y]=my_conv(x,h)
nx=length(x);
nh=length(h);
if (nx < nh)
y = my_conv(h,x);
else
ny=nx+nh-1;
y = zeros(1,ny);
for i =1:ny
idh = [max(i-(ny-nh),1):min(i,nh)]
idx = [min(i,nx):-1:max(nx-(ny-i),1)]
y(i) = sum(x(idx).*h(idh));
end
end
An alternate implementation which can be more computationally efficient for large arrays would make use of the convolution theorem and use the Fast Fourier Transform (FFT):
function [y]=my_conv2(x,h)
nx=length(x);
nh=length(h);
ny=nx+nh-1;
if (size(x,1)>size(x,2))
x = transpose(x);
end
if (size(h,1)>size(h,2))
h = transpose(h);
end
Xf = fft([x zeros(size(x,1),ny-nx)]);
Hf = fft([h zeros(size(h,1),ny-nh)]);
y = ifft(Xf .* Hf);