quiz 3 - EE 341 Quiz 3 Solutions 1(a n = 200k/500 = 400(b...

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EE 341 Quiz 3 Solutions 1. (a) n = 200 k/ 500 = 400. (b) The new carrier frequency is n × 110 k = 44 MHz. To obtain a carrier frequency of 100 MHz, use f LO = 56 or 144 MHz. (c) The BPF should have a center frequency of 100 MHz and a bandwidth of B FM = 2(Δ f + B ) = 2(200 + 10) k = 420 kHz. 2. (a) Since L = 2 n = 65536, the number of bits per sample is n = 16. The step size Δ = 2(2) / 65536 and the quantization noise is P Q = Δ 2 / 12. The SQNR is 10 log( . 5 /P Q ) = 92 . 07 dB. (b) The Nyquist rate is 30,000 samples/sec so that the minimum bit rate needed to encode the audio signal is 16 × 30 k = 480 kbps. (c) The practical sample rate is 44,100 samples/sec which is 47% higher than the minimum. This allows extra space in the spectrum so that the reconstruction filter does not have to be an ideal LPF and can have a rolloff. The LPF can be at its peak at 15 kHz and decrease to 0 at 22 kHz. (d) The minimum
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Unformatted text preview: bandwidth needed for practical audio is 44 , 100 × 16 / 2 = 352 , 800 Hz. 3. (a) Since g 1 ( t ) and g 2 ( t ) have infinite bandwidths, the bandwidths of y 1 ( t ) and y 2 ( t ) are 10 kHz and 15 kHz, respectively. Since Y ( f ) = Y 1 ( f ) * Y 2 ( f ), the bandwidth of y ( t ) is 25 kHz and the Nyquist rate is 50 kHz (50,000 samples/sec). (b) (i) The smallest setting of the local oscillator is 9 . 2 + . 455 = 9 . 655 MHz and the largest setting is 9 . 9 + . 455 = 10 . 355 MHz. (ii) Since the range of the broadcast band is 700 kHz and 2 f IF = 910 kHz, it is not possible for a desired station and its image station to be in the same band....
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