DFT and FFT for frequency analysis

Aims:1. Use MATLAB for DFT and FFT implementation2. Use MATLB for frequency analysisSuggestion procedure:All the lab work should be recorded in your logbook.1. Run MATLAB software from the Desctop. Find and records some functions for FFT in MATLAB.• The command fft will compute a discrete Fourier transform in Matlab. Type help fft to find out more.• Two more commands, ifft and ifftshift are needed to compute the inverse Fourier transform. Test the demo fft_demo.m2. Read and test MATLAB codes dft.m, mydft.m, dsp_fft.m in J:\V_Holmes\NHE2404 DSP Applications\Labs\matlab dsp\dft. Identify thedifference of coding and running time.3. Use MATLAB to analyse frequency component variations before and after filtering on a sound file of your choice (You may use thecodes in J:\V_Holmes\NHE2404 DSP Applications\Labs\matlab dsp\lab4q8_v.m).3. Use Internet search engine to search and download a FFT algorithm in C and try to understand the implementation of thealgorithm.Questions: Discuss the differences of DFT and FFT implementation in MATLAB or CTutorial Question1. A reson filter is required to have a resonant frequency of 5KHz and a bandwidth of 300Hz. The DSP ADC/DAC system has asampling frequency of 48KHz.a) Sketch the poles of the filter on a Z-plane diagram and show that the z-transfer function of the filter is:where R is the distance from the centre of the z-plane to each pole,  is the signal frequency and T the sampling time.b) Calculate the filter coefficients and write the difference equation for the filter.c) Determine the peak gain of the filter be in dB.