generate signals with different SNR

Hello all

I need to generate random white Gaussian noise of 3 second length. I also need to add 03 sinusoidal (say 10 KHz) pulses of 100 ms duration and SNRs of 1 dB, -10 dB and -20 dB respectively at random locations in 3 sec length Gaussian noise.

Can any one kindly help me with MATLAB code?

Also how can i verify the results i.e. the required SNR has been generated?

Thanks

[Image Analyst]

What's your sampling rate? How many elements do you want to use to represent this 3 second length?

[nauman]

My sampling rate is 100 K samples/s. This will result in 300 K samples for 3s length signal

[nauman]

Any help in this regard is highly appreciated plz.

Answer 1

[Shae Morgan]

Here's a solution! Hope it's helpful

%setup
fs=100000;
noise_dur=3;
sine_freq=10000;
sine_dur=.1;
t=0:1/fs:sine_dur-1/fs;
snr=[1,-10,-20];
sine_samps=sine_dur*fs;

%generate noise
noise=randn(fs*noise_dur,1); %generate gaussian noise
norm_noise=noise./max(noise); %scale noise
rms_noise=rms(norm_noise); %get the rms amplitude to which the sines will be compared

%generate the 3 signals at the 3 SNRs and check
for i=1:length(snr)
    amp=10^(snr(i)/20)*rms_noise;
    x=sin(2*pi*sine_freq*t);
    xt(i,:) = (x./rms(x)).*amp;
    check_snr=20*log10(rms(xt(i,:))/rms_noise)
end

%set random location 1
a=1;
b=length(noise)-sine_samps;
idx1=round(rand()*(b-a)+a);

%get random location 2 that doesn't overlap with 1
overlap=1;
while overlap==1
    idx2=rand()*(b-a)+a;
    if idx2<=idx1-sine_samps || idx2>idx1+sine_samps
        overlap=0;
    end
end
idx2=round(idx2);

%get random location 3 that doesn't overlay 1 or 2
overlap=1;
while overlap==1
    idx3=rand()*(b-a)+a;
    if idx3<=idx1-sine_samps || idx3>idx1+sine_samps 
        if idx3<=idx2-sine_samps || idx3>idx2+sine_samps 
        idx3=round(idx3);
            overlap=0;
        end
    end
end

%set the locations of the stimuli and pad zeros in between
[loc,idx]=sort([idx1 idx2,idx3]);
pad1=zeros(loc(1),1);
pad2=zeros(loc(2)-loc(1)-10000,1);
pad3=zeros(loc(3)-loc(2)-10000,1);
pad4=zeros(length(noise)-loc(3)-10000,1);
stim=[pad1; xt(idx(1),:)'; pad2; xt(idx(2),:)'; pad3; xt(idx(3),:)'; pad4];

%combine,play,and plot final sound
final=stim+norm_noise;
sound(final,fs)
plot(final) %stimulus is masked by the noise
plot(stim) %plot to see the stimuli

[nauman]

Thanks a lot for help. Kindly also tell how i can varify that these generated pulses are of required SNRs?

Thanks & Regards

[Shae Morgan]

That was included in the original answer. If you run the code, during the for-loop, it checks the SNR relative to the noise level and confirms each generated sine is of the appropriate level with reference to the noise.

%generate the 3 signals at the 3 SNRs and check
for i=1:length(snr)
    amp=10^(snr(i)/20)*rms_noise;
    x=sin(2*pi*sine_freq*t);
    xt(i,:) = (x./rms(x)).*amp;
    check_snr=20*log10(rms(xt(i,:))/rms_noise) %<----this line
end

If this answer has been useful, please accept.

Thanks!

[Shae Morgan]

If you want to make sure that the local SNR is exact, you'll need to find the RMS of the samples of noise at the times where the tones are played, and then set the amplitude of the sine waves based on a comparison there.

[Daniel May]

I believe:

final=stim+noise;

should be:

final=stim+norm_noise;

-Daniel

[Shae Morgan]

@Daniel - thanks for catching! I updated to reflect this

Answer 2

[nauman]

Hi all

Any help plz?

Thanks