【正文】
, (c) .(2) Sketch the sequence whose 8point DFT is given by . denote the Npoint circular convolution .Determine the values of ,. Explain which value is equal to the value of. Sketch the linear convolution .(2) (2) Determine the value of .4. Let ={1 2 1 1},and ={1 1 1},. (1) (1) . (3) (3)3. A real 8point sequence .Its 8point DFT is X[k].(1) Determine the values of ,.(2) (2)Test Of Digital Signal Processing2Give the answer of the following problems in English as possible as you can.1. Determine the fundamental period of sequence .)。title(39。Gain, dB39。)。xlabel(39。plot (omega/pi,20*log10(abs(h)))。[N,Wn] = ellipord(Wp,Ws,Rp,Rs)[b,a] = ellip(N,Wn)。Minimum stopband attenuation in dB = 39。)。Rp = input(39。Normalized stopband edge = 39。)。 Develop a realization of the system in any canonic form.5. Design a FIR linear phase causal LPF which has cutoff frequency , transition bandwidth and minimum stopband attenuation .Develop the impulse response in closed form by Windowed Fourier Series method. you use following MATLAB program to design a lowpass filter ,which has the specifications:passband edge 800Hz ,stopband edge 1kHz, passband ripple , minimun stopband attenuation 40dB ,and sampling rate is data should you input to the puter?% Program For Elliptic IIR Lowpass Filter Design%Wp = input(39。 Give the polezero plot and the ROC of the system.(3) 3. A sequence has the 128point DFT. Give the expression of . 4. A causal LTI discretetime system has the transfer function .(1)Test Of Digital Signal Processing 1Give the answer of the following problems as possible in English.1. Supposing when and .Please give its ZT , DTFTand Npoint DFT .Explain the relations among these three transforms .2.(10分)已知X(z)=,分別求 (1)|z|2時(shí)的原序列x(n)(2)收斂域?yàn)椋鼁|2時(shí)的原序列x(n)3.(10分)濾波器的單位抽樣響應(yīng)為h(n)=u(n)u(n4),求其系統(tǒng)函數(shù),畫出其橫截型結(jié)構(gòu)圖。用一個(gè)已給出N點(diǎn)的復(fù)數(shù)FFT程序,一次算出(即的2N點(diǎn)DFT)。(3) 已知,求小(n)。(2) N選奇數(shù)好還是選偶數(shù)好?為什么?(3) 若改用生余弦窗設(shè)計(jì),求的表達(dá)式。并畫出該濾波器的結(jié)構(gòu)圖。四、(10分)設(shè)采樣頻率,用脈沖響應(yīng)不變法設(shè)計(jì)一個(gè)三階巴特沃斯數(shù)字低通濾波器。試證明:三、(12分)已知,若為線性卷積,而,分別是周期為10的圓周卷積。并解釋這兩種情況的原因。(1)當(dāng)時(shí),求輸出。(2) 求x(n)的4點(diǎn)DFT :X(K);(3) 求x(n)的8點(diǎn)DFT :X(K);(4) 你能從序列的DFT和FT之間的關(guān)系中,得出什么結(jié)論?令H1(z)=+H2(z)=H3(z)= H1(z) /H2(z)(1) 畫出H1(z)直接實(shí)現(xiàn)的信號(hào)流圖(2) 畫出H3(z)直接實(shí)現(xiàn)的信號(hào)流圖(3) H1(z)和 H3(z)分別代表何種類型的數(shù)字濾波器?一、(8分)下面所示理想采樣數(shù)字處理系統(tǒng)。1z1H(Z)= —————— 12z13z2五.設(shè)模擬濾波器的系統(tǒng)函數(shù)為 2 1 1 Ha(s)=—————= ———— ———— S2+4s+3 s+1 s+3 試分別利用沖激響應(yīng)不變法和雙線性變換法,設(shè)計(jì)IIR數(shù)字濾波器。請(qǐng)畫出8點(diǎn)的按頻率抽取的(DIF)基2 FFT流圖,要求輸入自然數(shù)順序,輸出倒位序,并以此畫出DITIDFT流圖2 設(shè)序列x(n)=R(n) (n) = (30 試作圖表示x(n),(n) 已知另一序列h(n) =R(n), (1)試求線性卷積 (2)和5點(diǎn)圓周卷積。(3)試求8點(diǎn)循環(huán)卷積。 求x(n)=anu(n)的傅里葉變換FT。( )三、計(jì)算題(每題5分)δ(n+4)*u(n