where could my error

numSamples = 250;

t = linspace(0,50,numSamples);

x = sin(2*pi*100*t) + 0.7*cos(2*pi*500*t);

xn = x + 5.*randn(size(t));

Answer 1

[Star Strider]

I bellieve ‘NumSamples’ should be larger.

Try this —

Fs = 5000;                                                      % <- ADDED
Fn = Fs/2;                                                      % <- ADDED
numSamples = 250*Fs;                                            % <- CHANGED
t = linspace(0,50,numSamples);
x = sin(2*pi*100*t) + 0.7*cos(2*pi*500*t);
xn = x + 5.*randn(size(t));
originalSpectrum = fft(x); 
noisySpectrum = fft(xn);
Fv = linspace(0, 1, fix(numel(t)/2)+1)*Fn;                      % One-Sided Fourier Transform Frequency Vector
Iv = 1:numel(Fv);                                               % Corresponding Index Vector

figure
subplot(4, 1, 1);
plot(Fv, abs(originalSpectrum(Iv))*2, 'b-', 'LineWidth', 2);
grid on;
xlabel('t');
ylabel('x');
subplot(4, 1, 2);
plot(Fv, abs(noisySpectrum(Iv))*2, 'b-', 'LineWidth', 2);
dee = designfilt('lowpassfir', 'PassbandFrequency', 500, ...
                 'StopbandFrequency', 600, ...
                 'PassbandRipple', 1, 'StopbandAttenuation', 100, ...
                 'SampleRate', 5000);
dataOut = filter(dee,xn);
subplot(4, 1, 3);
plot(dataOut);
trfcn = fft(dataOut)./noisySpectrum;
subplot(4,1,4)                                                  % <- ADDED
plot(Fv, abs(trfcn(Iv)))
title('Transfer Function Of Filter')

I did not change anything of significance, just added some tweaks to make it a bit easier to understand.