Help required in matlab

Can you help me with the following :
I'm supposed to prove the modulation theorem which states that multiplication in time domain is interpreted as convolution in frequency domain:

suppose we have
xn : first signal
yn : second signal

n_x = length(xn); %length of first sig.
n_y = length(yn); % length of second signal

m = min(n_x,n_y);
xy = xn(1:m) .* yn(1:m);

xf = fft(xn,N);
yf = fft(yn,N); %where N is chosen suitably as a power of two and greater than
% max(n_x,n_y)
xy_new = fft(xy,K);
%how could i verify that xy_new equals conv(xf,yf)

if someone knows how could i solve this i would be thankful

hi,

i will explain this by a suitable example.

u want to proove "modulation theorem which states that multiplication in time domain is interpreted as convolution in frequency domain"

conversely let me state it as convolution in the frequency domain can be interpreted as multiplication in the time domain.

let me take the following Fourier transform pairs

x <==> X(k) y <==> Y(k)
FT FT

let X(k) be of length p, and,
Y(k) be of length q

and, let N = p+q-1

x is the N point IFFT of X(k)
similarly,
y is the N point IFFT of Y(k)

it can be easily proved that,
conv(X(k),Y(k)) = FFT(x .* y)

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probably what you have missed is the zero padding part
before taking IFFT..