# Category: signal processing and linear systems #### Problem 3.15 Let Determine the relationship between xn and the following IDFT’s:

... #### Problem 3.14 Let . Determine the relationships between and the following DFT’s:

... #### Problem 3.13 A problem in many software packages is that you have access only to positive indexes. Suppose you want to determine the DFT of the sequence with the zero index as shown, and the DFT algorithm let you compute the DFT of a sequence like , what do you do?

... #### Problem 3.12 You know that the DFT of the sequence . Now consider two sequences: both of length

... #### Problem 3.11 You know that DFT Use the minimum number of operations to compute the following transforms:

... #### Problem 3.9 Let x be a finite sequence with DFT Using the properties of the DFT determine the DFT’s of the following:

... #### Problem 3.8 Two finite sequences h and x have the following DFT’s: Let y = h≈ x be the four point circular convolution of the two sequences. Using the properties of the DFT (do not compute xn and hn), a) determine DFT b) determine y0 and y1.

... #### Problem 3.7 Two finite sequences have DTFs given by Using the properties of the DFT (do not compute x and h explicitly , compute the following :

... #### Problem 3.4 Let be the DTFs of two sequences x and h respectively. Using the properties of the DFT (do not compute the sequences) determine the DFTs of the following :

... #### Problem 3.3 Compute the DFT of the following sequences

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