Show Equivalence Between Multiplication in Time Domain to Convolution in Frequency Domain
Let's assume you have 2 signals: vX and vY.
So:

clear();

numSamplesX = length(vX);
numSamplesY = length(vY);

numSamplesConv = numSamplesX + numSamplesY - 1;

vTimeDomainConv = conv(vX, vY);

vFrequencyDomainConv = ifft(fft(vX, numSamplesConv) .* fft(vY, numSamplesConv), 'symmetric');

max(abs(vTimeDomainConv - vFrequencyDomainConv)) %&lt;! Should be &lt; 1e-12


This is the Convolution Theorem for Discrete Signals to show convolution in time domain is equivalent to element wise multiplication in frequency domain.

If you want to show element wise multiplication in time domain can be done using the convolution in frequency domain you need to either interpolate the time domain signal to length of linear convolution or just use circular convolution in frequency domain:

clear();

numSamples = 6;

vX = randn(numSamples, 1);
vY = randn(numSamples, 1);

vXY = vX .* vY; %&lt;! Time Domain Mulaiplication
vDxy = fft(vXY); %&lt;! The DFT of the Time Domain Multiplication

vDx = fft(vX);
vDy = fft(vY);

% Applying circular convolution
vXYC = cconv(vDx, vDy, numSamples) / numSamples; %&lt;! Normalization

% Comparing the result in Frequency Domain
max(abs(vXYC - vDxy)) %&lt;! Should be &lt; 1e-12

% Time Domain
vXYFromFrequency = ifft(vXYC, 'symmetric');

% Comparing the result in Time Domain
max(abs(vXY - vXYFromFrequency)) %&lt;! Should be &lt; 1e-12