Signal Processing and Linear Systems-B.P.Lathi copy

I n o ther words t he s pectrum should be sampled a t

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: if you -' ". .3 "'{).1 0 '" 0.2 '~'. t --- Fig. P 5.1-7 F lat t op s ampling. 5 .1-7 I n E xample 5.3, t he s ampling of a signal j (t) was accomplished by multiplying t he signal by a pulse t rain PT(t), r esulting in t he s ampled signal depicted in Fig. 5.8d. T his p rocedure is known as t he n atural s ampling. F igure P 5.1-7 shows t he so called f lat t op s ampling o f t he s ame signal j (t) = sinc 2(51l"t). ( a) Show t hat t he signal j (t) c an b e recovered from fiat t op s amples if t he s ampling r ate is no less t han t he N yquist rate. ( b) E xplain how you would recover j et) from t he fiat t op samples. ( c) F ind t he expression for t he s ampled signal s pectrum F(w) a nd sketch i t roughly. Hint: F irst show t hat t he fiat t op s ampled signal c an b e generated by passing t he signal j(t)OT(t) t hrough a filter whose impulse response is h (t) = p T(t). For signal recovery from t he samples, follow t he reverse procedure. 5 .1-8 A c ompact disc ( CD) r ecords audio signals digitally by using P CM. Assume t he a udio signal b andwidth t o b e 15 kHz. ( a) W hat is t he N yquist rate? ( b) I f t he N yquist samples are quantized into 65536 levels ( L = 65536) a nd t hen b inary-coded, w hat n umber o f b inary digits is r equired to encode a sample. ( c) D etermine t he n umber o f binary d igits/s ( bits/s) r equired t o e ncode t he a udio signal. ( d) For practical reasons discussed in t he t ext, signals are sampled a t a r ate well above t he N yquist rate. P ractical CDs use 44100 samples/so I f L = 65536, determine t he n umber of pulses/ s required to encode t he signal. 5.1-9 A T V signal (video a nd audio) h as a b andwidth o f 4.5 MHz. T his signal is s ampled, quantized a nd b inary-coded t o o btain a P CM (pulse code modulated) signal. ( a) D etermine t he s ampling r ate if t he signal is t o b e sampled a t a r ate 20% above t he N yquist rate. ( b) I f t he s amples a re q uantized into 1024 levels, w hat n umber of binary pulses is required to encode each sample. ( c) D etermine t he b inary pulse r ate ( bits/s) o f t he b inary coded signal. 3 60 5 S ampling - 10 Prove t hat a s ignal cannot be simultaneously timelimited and bandlimited. Hint: Show t hat contrary assumption leads to contradiction. Assume a signal simultaneously timelimited and bandlimited so t hat F(w) = 0 for Iwl > 27rB. I n this case F(w) = F (w)rect (4,,"'B1) for B ' > B. This fact means t hat J(t) is equal t o J(t) * 2 B'sinc(27rB't). The latter cannot be timelimited because the sine function tail extends to infinity. ~-1 For a signal Jet) t hat is timelimited to 10 ms and has an essential bandwidth of 10 kHz, determine No, the number of signal samples necessary t o compute a power of 2-FFT with a frequency resolution Fa of a t least 50 Hz. Explain if any zero padding is necessary. Continuous-Time S ystem Analysis U sing t he Laplace T ransform I~ 2 -2 To compute t he D FT of signal J(t) in Fig. P5.2-2, write the sequence !k (for k = 0 to No - 1) if the frequency resolution Fa mu...
View Full Document

This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

Ask a homework question - tutors are online