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Lesson_34 - Lesson34 Challenge33 (DFT NoChallengeProblem...

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Lesson 34 Lesson 34 Challenge 33 Lesson 34 – Discrete Fourier Transform (DFT) No Challenge Problem Practice Quiz #3 next meeting
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  Lesson 34 Challenge 34 An AN-DSB superheterodyne receiver is shown in the figure and  consists of an antenna, RF amplifier, mixer, local oscillator (LO)  producing a variable frequency signal x(t)=cos( ϖ 0 t), an intermediate  frequency (F) amplifier having a fixed center-frequency of 455kHz and  bandwidth of 10kHz. and finally an envelop detector.  What must be  the tuning range of the local oscillator in order to operate properly?  x(t) y(t) Local Oscillator (LO) RF Amp IF Amp Det. Envelope Detector z(t) Output
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  Lesson 34 Lesson 33 Table 1: Commercial Radio Item AM FM Carrier frequency 540-1600 kHz 88.1-107.9 MHz Transmission Bandwidth 10kHz 200kHz Audio bandwidths 3-5kHz 15kHz Using the difference frequencies, the LO range must be:   2 πϖ c ={540-455 = 85 kHz to 1600-455=1145 kHz} Using the sum frequencies, the LO range must be:   2 πϖ c ={540+455 = 995 kHz to 1600+455=2055 kHz}
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  Lesson 34 Lesson 34 Continuous-time Fourier transform  (CTFT)  - - = dt e t x X t j ϖ ϖ ) ( ) (j - = ϖ ϖ π ϖ d e X t x t j ) (j 2 1 ) (
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  Lesson 34 Lesson 34 Continuous-time   Fourier series  (CTFS)   - = T t jn p n dt e t x T c 0 0 0 ) ( 1 ϖ -∞ = = n t jn n p e c t
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