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# Homework 10 ECE 310 Relevant Chapters: 4, 5, 12, 7, 6 1. Circle TRUE or FALSE: The DTFT is used to transform discrete-time signals to the frequency...

Homework 10 ECE 310 Relevant Chapters: 4, 5, 12, 7, 6 1. Circle TRUE or FALSE: The DTFT is used to transform discrete-time signals to the frequency domain. 2. Circle TRUE or FALSE: The DFT is used to transform all discrete-time signals to the frequency domain. 3. Circle TRUE or FALSE: The TFT is an efficient implementation of the DFT. 4. Circle TRUE or FALSE: Whenever a signal is periodic in the time domain, its spectrum will also be discrete in the frequency domain 5. Circle TRUE or FALSE: The spectrum of a discrete (sampled) signal will be discrete. 6. Circle TRUE or FALSE: If a signal's spectrum is discrete and periodic (in frequency), then the original signal was also discrete and periodic (in time). 7. How many times faster than the DFT would you expect an FFT algorithm to execute when the number of samples being transformed is ° = 2 8 ? 8. Circle TRUE or FALSE: Recovering the original signal spectrum from sampled spectrum does not require a perfect ideal lowpass reconstruction filter if sampling was done at the Nyquist rate. 9. Circle TRUE or FALSE: Pre-filtering x(t) so there is no energy above ± ² /2 before sampling will guarantee that no aliasing will occur and the entire original signal spectrum (and therefore the entire original signal x(t)) can be recovered. 10. Circle TRUE or FALSE: A single resistor and a single capacitor can be used in a circuit to construct a simple (non ideal) lowpass filter frequency response. 11. What is the frequency response of the sytem having ?(³) = ´?µ¶· ¸¹º{»(³)} , passing all frequencies above 10 rad/sec? 12. Circle TRUE or FALSE: A discrete-time LSI (linear shift invariant) system with impulse response h(n) will have a periodic frequency response. 13. Circle TRUE or FALSE: You can create a digital lowpass filter that can attenuate all higher frequencies outside of its bandwidth.

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8. FALSE
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10. TRUE 11. 12. TRUE
13. FALSE , the FFT is 8 times faster than the DFT.

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