Question

In: Computer Science

Develop the 8-point Discrete Fourier Transform (DFT) using butterfly diagrams for the discrete input sequence x(n)...

Develop the 8-point Discrete Fourier Transform (DFT) using butterfly diagrams for the discrete input sequence x(n) = {1, 2, 3, 4, 4, 3, 2, 1} using radix-2 Decimation in Frequency - Fast Fourier Transform (DIF-FFT) algorithm.

Solutions

Expert Solution

So DIF for x(n)

X(n) = {20 , -5.828-2.414j , 0 , -0.172-0.414j , 0 , -0.172+0.414j , 0 , -5.282+2.414j}


Related Solutions

(TCO 7) What is the difference between discrete Fourier transform (DFT) and fast Fourier transform (FFT)?...
(TCO 7) What is the difference between discrete Fourier transform (DFT) and fast Fourier transform (FFT)? can you please type it cant see images.
Find the 10-point DFT sequence of the x [n] sequence given below. ?[?] = cos (...
Find the 10-point DFT sequence of the x [n] sequence given below. ?[?] = cos ( 3??/ 5 ) . sin( 4??/ 5 )
Both the Fourier Series and the Discrete Fourier Transform are calculated using summation. Explain the key...
Both the Fourier Series and the Discrete Fourier Transform are calculated using summation. Explain the key differences in what the inputs each of the Fourier Series and the DFT are AND the requirements the inputs.
Use MATLAB to find the 8 point DFT of x(n) = cos(2πmn/8) (m=3) for 0 ≤...
Use MATLAB to find the 8 point DFT of x(n) = cos(2πmn/8) (m=3) for 0 ≤ n ≤ 7. Plot both x(n) and its DFT and explain your results. The "dct" and "fft" functions in MATLAB may be useful. Please post MATLAB code.
4. For a signal x(n)=sin(2*pi*n/3) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow...
4. For a signal x(n)=sin(2*pi*n/3) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow graph. (Use decimation in frequency Algorithm)     
For a signal x(n)=sin(2*pi*n/5) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow graph....
For a signal x(n)=sin(2*pi*n/5) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow graph. (Use decimation in Time Algorithm).                                               
4. For a signal x(n)=sin(4*pi*n/5) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow...
4. For a signal x(n)=sin(4*pi*n/5) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow graph. (Use decimation in Time Algorithm).                                                
For a signal x(n)=sin(2*pi*n/5) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow graph....
For a signal x(n)=sin(2*pi*n/5) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow graph. (Use decimation in Time Algorithm).                                               
a) Find the discrete Fourier series (DFS) representation of x((n))10, where 10 denotes the period and...
a) Find the discrete Fourier series (DFS) representation of x((n))10, where 10 denotes the period and x(n) is given by: ?(?) = { 1, ??? 0 ≤ ? ≤ 5 0, ??? ??ℎ?? ? b) For the following two causal sequences (both starting at n = 0), find the circular convolution of minimum size that will produce the same result as h(n)*x(n). h(n) = {1, 1, 1, 1}, x(n) = {0, 0, 1, 1}
Consider the following periodic signal : x(t)=∑∞n=−∞Π(t−4n2). 1. Determine and plot the spectrum Fourier Transform of...
Consider the following periodic signal : x(t)=∑∞n=−∞Π(t−4n2). 1. Determine and plot the spectrum Fourier Transform of signal x(t) ( For plot : Use only interval n=-2 to n=2). 2. Based on the result obtained in part one. Determine Complex Exponential Fourier Series, and trigonometric Fourier Series. 3. Evaluate the energy spectral density of the periodic signal x(t) in rang (n=-2 to n=2)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT