Matlab: Mean Square Error

Hi I am new to Matlab and I am having difficulties understanding the logic behind Mean Square Error. I have been given a signal and I am able to generate it and calculate SNR of the signal, is there a way to find mean square error between original signal and SNR signal?

% Number of Samples.

n = 1:512;

% Given Signal

signal = exp(-5*(n-250).^2/100000).cos(pi(n-250)/6);

% Range of SNR

Snr = 30:-5:-10

% Calculate and display MSE between the original signal and noisy signal

??????

[Adam]

Which part of it do you not understand?

• Calculate the error (subtraction)
• Square it
• Apply a mean filter to the result with a filter size you feel appropriate

would be the usual process I imagine.

[Ali Arslan]

Hi Adam Thanks for reply I don't understand

How to calculate the error (subtraction) How to calculate the error (subtraction) Square it Please Recommend me how I can calculate mean square error here thanks

Following Code I am using

%% Generate a Noisy Signal.

% Number of Samples

n = 1:512;

% Given Signal

signal = exp(-5*(n-250).^2/100000).*cos(pi*(n-250)/6);

% Range of Signal to Noise ratio

Snr = (30:-5:-10);

for snr = 1:length(Snr)

    noisy_signal = awgn(signal,Snr(snr),'measured');
    end
end

figure(); plot(signal); title('Input signal'); grid on;

figure(); plot(noisy_signal); title('Signal With Noise'); grid on;

[Adam]

I'm still not sure exactly what aspect you are struggling on.

signal - noisy_signal;

is a subtraction.

a.^2

is a squaring of the an array a.

The Mathlab documentation includes plenty of help on applying a simple mean filter to the result of that.

Answer 1

[Image Analyst]

If you have the Image Processing Toolbox, use immse() or psnr().

[Ali Arslan]

I am working on problem mentioned below, what do you suggest about solving this problem thanks

generate noisy signals by embedding a Gaussian envelope sinusoidal signal of 512 samples given by sn = exp[−5(n−250)2/100000]cos[π(n−250)/6] in the zero-mean additive white Gaussian noise in various signal-to-noise (SNR) settings, and display the noisy signal waveforms produced with the corresponding SNR from 30 dB to −10 dB at approximately 5 dB intervals and mean-squared errors (MSE) between the original signals and noisy signals.

[Image Analyst]

I suggest you make an n with linspace(), and plug it in

n = linspace(0, 50000, 512);
sn = exp(-5*(n-250)* 2/100000) .* cos(pi *(n - 250) / 6);
plot(n, sn, 'b*-');
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')

Note: this is a badly aliased signal as you can see by increasing the number of samples from 512 to 1000 to 5000 to 10000 or more. The period of the cosine wave is 12 so you should have at least one sample every 3 units to not have bad aliasing.

[Ali Arslan]

Thank you so much for helping me out.

Now I understand the concept behind it but I am still struggling to solve Mean Square Error Problem as you read in my question which I posted above, I have to calculate a mean square error between original signal and noisy signal. How can I solve this problem thanks?

[Image Analyst]

Like Adam, I'm confused why this is so complicated and confusing to you. The name tells you how to do it. Let me do it in multiple steps.

Get the error

theError = signal - noisySignal;

Square it

squaredError = theError .^ 2;

Get the mean

% Use the mean() function.

I can't do every single step for you because it sounds like homework but the last step is unbelievably trivial.

One thing to get clarification on from your instructor is if the SNR is calculated based on the maximum signal, or is is supposed to apply on a element by element basis, which means the noise on the right will be less than on the left because the signal decays.