Guidance with DFT Transform

I need help with implement DFT transform i am attaching the function i should do the DFT. i need guidance and code example.

thanks a lot Moshe

Answer 1

[Kevin]

f = 10;  % 10 Hz.
t = (0:2047)/100; % 100 Hz sampling rate.
x = sin(2*pi*f*t);
X = fft(x);

Answer 2

[Moshe]

First of all thanks for you quick answer. from your guidance i wrote this matlab code implement DFT. See source code:

f0=46.875;

W0=2*pi*f0;

Fs=1000;

T=1/Fs;

NFFT=512;

FFTperiod=NFFT*T;

t=(0:NFFT-1)*T;

str=['FFT period is ',num2str(FFTperiod), ' seconds'];

Freq=10*1/FFTperiod

strFreq =['Frequency is ', num2str(Freq), ' Hz'];

Freqbin =1/FFTperiod

strFreqbin =['FFT frequency bin is ',num2str(1/FFTperiod), ' Hz'];

strFreqNyquist =['FNyquist is ',num2str(1/FFTperiod*512), ' Hz'];

disp(str);

disp(strFreq);

disp(strFreqbin);

disp(strFreqNyquist);

x_t=sin(W0*t);

subplot(3,1,1)

plot(t,x_t);

title('time domain signal')

xlabel('Time')

ylabel('Amplitude')

Z=fft(x_t,NFFT)/NFFT;

f=Fs/2*linspace(0,1,NFFT/2);

subplot(3,1,2);

plot(f,abs(Z(1:NFFT/2)))

title('freq domain')

xlabel('Hz')

ylabel('Amplitude')

now i would like to add zero padding and plotting it to a graph and i am not success.

can some one advise me?