How do i do this in MATLAB?

I've got 2 noise vectors(x1 and x2) that I need to add to the pwelch command but I can't figure out what's wrong with my code. How do I add the 2 vectors together for the pwelch command? please help. code is below

f1 = 4000;        %sinusoidal frequency
A1 = 0.2;         %amplitude
f2 = 5000;        %sinusoidal frequency
A2 = 0.25;       %amplitude
t1 = 0:1/f1:5-1/f1;
t2 = 0:1/f2:5-1/f2;
x1 = A1*cos(2*pi*f1*t)+randn(size(t1));
x2 = A2*cos(2*pi*f2*t)+randn(size(t2));
x = x1+x2;
[y,Fs]=audioread('doorbell.wav');
[pxx,f] = pwelch(x,500,300,500,Fs);
plot(f,10*log10(pxx)); xlabel('Frequency (Hz)'); ylabel('PSD (dB/Hz)');

Answer 1

[Walter Roberson]

>> size(t1)
ans =
           1       20000
>> size(t2)
ans =
           1       25000

Your x1 is the same size as t1, and your x2 is the same size as t2. x1+x2 is therefore attempting to add a vector of length 20000 and a vector of length 25000.

You are using the wrong approach.

f1 = 4000;        %sinusoidal frequency
A1 = 0.2;         %amplitude
f2 = 5000;        %sinusoidal frequency
A2 = 0.25;       %amplitude
secs = 5;

N = lcm(f1*secs, f2*secs);   %lowest common multiple
t = linspace(0, secs, N+1);
t(end) = [];
x1 = A1*cos(2*pi*f1*t)+randn(size(t));
x2 = A2*cos(2*pi*f2*t)+randn(size(t));

You should consider whether the randn should be at full magnitude or should be multiplied by A1 or A2 . As it is you have 5 times as much noise as you have signal for x1.

You do not really need the full lcm() samples over 5 seconds, but using the lcm() ensures that there are an exact integer number of cycles for each of f1 and f2 in those 5 seconds.

I am, though, seeing some clipping in cos(2*pi*f1*t) that I cannot quite explain at the moment.