dft implementation

write the Matlab code (not using built-in function, such as fft, abs, angle) to draw the spectrum of impulse signal in terms of real and imaginary part, magnitude and phase. As for the impulse signal given in the handout, the real part of DFT result are cosine sequence, the imaginary part are (minus) sinusoidal sequence. The magn itude are constantly 1, where the phase are exponential sequence. The period is 16 sequences (full length of samples). When I delay the impulse signal with 1 sample, the four items (real,imaginary, magnitude, phase) didn't change their contours but the periods reduced to their half length (8 sequences). This is because the DFT result will multiply exp(-j*2*pi*k/N) /N with 1 shift for the impulse signal and consequently the DFT result with 1 sample delayed became exp(-j*2*pi*2*k/N) /N . When we delay the impulse by 2 samples, the DFT result would become exp(-j*2*pi*3*k/N) /N. The counter will remain and the period will become length/3 (16/3). itude are constantly 1, where the phase are exponential sequence. The period is 16 sequences (full length of samples). When I delay the impulse signal with 1 sample, the four items (real,imaginary, magnitude, phase) didn't change their contours but the periods reduced to their half length (8 sequences). This is because the DFT result will multiply exp(-j*2*pi*k/N) /N with 1 shift for the impulse signal and consequently the DFT result with 1 sample delayed became exp(-j*2*pi*2*k/N) /N . When we delay the impulse by 2 samples, the DFT result would become exp(-j*2*pi*3*k/N) /N. The counter will remain and the period will become length/3 (16/3).