Problem 2.19 Consider the passband signal upl) = sinc(,) cos(20 t, where the uni

Question

Problem 2.19 Consider the passband signal upl) = sinc(,) cos(20 t, where the unit of time is in microseconds 1001, s'i,».ila (a) Use MATLAB to plot the signal (plot over a large enough time interval so as to include "most" of the signal energy). Label the units on the time axis.

Explanation / Answer

octave:1> Decimation Filter Design ddc.MinimumOrderDesign = true; The down converter processes a signal with a two-sided bandwidth of 160 KHz. Set the Bandwidth property of the DDC object to 160 KHz so that the passband frequency of the decimation filter cascade equals 160e3/2 = 80 KHz. Set the Stopband FrequencySource property to 'Auto' so that the DDC object sets the cutoff frequency of the cascade response approximately at the output Nyquist rate, i.e. at 270.83e3/2 = 135.4 KHz, and the stopband frequency at 2Fc-Fpass = 2*135.4e3 - 160e3/2 = 190.8 KHz, where Fc is the cutoff frequency and Fpass is the passband frequency. When you set Stopband FrequencySource to 'Auto', the DDC object relaxes the stopband frequency as much as possible to obtain the lowest filter orders at the cost of allowing some aliasing energy in the transition band of the cascade response. This design layout is convenient when your priority is to minimize filter orders. ddc.Bandwidth = 160e3; % Passband frequency equal to 80 KHz ddc.StopbandFrequencySource = 'Auto'; % Allow aliasing in transition band Finally, set a stopband attenuation of 55 dB and a passband ripple of 0.04 dB. ddc.StopbandAttenuation = 55; ddc.PassbandRipple = .04; Get the designed filter orders and the coefficient word lengths for the CIC compensator and third stage FIR design. ddcFilters = getFilters(ddc,'Arithmetic','Fixed-point'); n = getFilterOrders(ddc); CICCompensatorOrder = n.SecondFilterOrder ThirdStageFIROrder = n.ThirdFilterOrder CICCompensatorCoefficientsWordLength = ... ddcFilters.SecondFilterStage.CustomCoefficientsDataType.WordLength ThirdStageFIRWordLength = ... ddcFilters.ThirdFilterStage.CustomCoefficientsDataType.WordLength CICCompensatorOrder = 12 ThirdStageFIROrder = 18 CICCompensatorCoefficientsWordLength = 11 ThirdStageFIRWordLength = 11 If aliasing in the transition band is not acceptable, set the stopband frequency to an arbitrary value by setting the StopbandFrequencySource property to 'Property'. Obtain a narrower transition band by setting the stopband frequency to 128 KHz at the expense of a larger third stage filter order. ddc.StopbandFrequencySource = 'Property'; ddc.StopbandFrequency = 128e3; close(fvt) fvt = fvtool(ddc,'Arithmetic','fixed-point'); Processing Loop Initialize a sine wave generator to simulate a GSM source. Initialize a buffer to cast the input signal data type to 19 bits word length and 18 bits fraction length. Configure figures for plotting spectral estimates of signals. Fs = 69.333e6; FrameSize = 768; sine = dsp.SineWave('Frequency', 14.44e6+48e3, 'SampleRate', Fs, ... 'PhaseOffset', 0, 'SamplesPerFrame', FrameSize); gsmsig = fi(zeros(FrameSize,1),true,19,18); inputSpectrum = dsp.SpectrumAnalyzer( ... 'SampleRate',sine.SampleRate, ... 'SpectralAverages',10, ... 'Title','Power spectrum of input signal'); outputSpectrum = dsp.SpectrumAnalyzer( ... 'SampleRate',sine.SampleRate/ddc.DecimationFactor, ... 'SpectralAverages',10, ... 'Title','Power spectrum of down-converter signal'); Main simulation loop for ii = 1:1000 % Create GSM signal with 19 bits of word length and 18 bits of fraction % length. gsmsig(:) = sine(); % Down convert GSM signal downConvertedSig = ddc(gsmsig); % Frequency domain plots inputSpectrum(gsmsig); outputSpectrum(downConvertedSig); end % Release objects release(sine); release(ddc); release(inputSpectrum); release(outputSpectrum); >>> CICCompensatorOrder = ^ ans = 12 >>> ThirdStageFIROrder = ^ ans = 18 >>> CICCompensatorCoefficientsWordLength = ^ ans = 11 >>> ThirdStageFIRWordLength = ^ ans = 11

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