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# Keee4314 1 2012

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contoh soalan peperiksaan akhir semester tahun 2012 bagi subjek Digital Signal Processing.

past years question of Digital Signal Processing

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### Keee4314 1 2012

1. 1. UNIVERSITI MALAYA UNIVERSITY OF MALA YA PEPERIKSAAN IJAZAH SARJANA MUDA KEJURUTERAAN EXAMINATION FOR THE DEGREE OF BACHELOR OF ENGINEERING SES! AKADEMIK 2011/2012 : SEMESTER 1 ACADEM/ C SESSION 2011/2012 . ' SEMESTER 1 KEEE 4314 : PEMPROSESAN ISYARAT DIGIT DIGITAL SIGNAL PROCESSING JANUARI 2012 MASA: 2 JAM JANUARY 2012 TIME: 2 HOURS ARAHAN KEPADA CALONI INSTRUCTIONS TO CANDIDA TES: Calon dikehendaki menjawab SEMUA soalan Candidate must answer ALL the question (Kertas soalan ini mengandungi 5 soalan dalam 6 halaman yang dicetak) (This question paper consists of 5 questions on 6 prïnted pages)
2. 2. KEEE 4314/02 SOALAN 1/ QUESTION 1 (a) Cari konvulasi dan piotx[n] * h[n]yang diberi dí bawah: Compute and plot the convolution of x[n] * h[n] given below: x[n] = _n u[-n - l] h[n] = u[n - l] (4 markah/ marks) (b) Mempertimbangkan dua sistem LTI dengan sambutan sampel unit Consider two LTI systems with the unit sample responses h, [n] = í- šïødn] and h2[n]= w[n] + šuhz - 1]. Kedua sistem bergabung bersiri yang ditunjuk dalam gambarajah 1 di bawah: These systems are cascaded as shown / `n Figure 1 below. Gambarajah 1/Figure 1 Di beri x[n] = u[n]. Let x[n] = u[n]. i) Cari w[n] dan y[n] Compute w[n] and y[n] ii) Dapatkan sambutan dedenyut keseluruhan h[n] = (h[n] * (h[n] Determine the overall impulse response h[n] = h . m : k (h[n]
3. 3. KEEE 4314103 iii) Dapatkan y[n] = x[n] * h[n] Determine y[n] = x[n] * h[n] (8 markahlmarks) SOALAN 2/ QUESTION 2 (a) Carikan sambutan keluaran sifar, sambutan masukan sifar dan jumlah sambutan untuk sistem berikut yang diberi dalam persamaan pembeza dengan mengguna transformasi-Z: Find the zero-state response, zero-input response and total response for the following system described by its difference equation using the Z-transform : y[n] - y[n -1] + O.5y[n - 2] = O.5"u[n] y[-1] = -1. y[-2]= -2. (4 markahlmarks) (b) Lakarkan plot kutub sifar dan sambutan frekuensi untuk sistem-sistem berikut yang diberi dalam sambutan dedenyut dan rangkap pindah. Sketch the pole-zero plot and frequency response of the following systems described by its impulse response and transfer function = '11 } (3 markahlmarks) (c) Cari pekali siri Fourier untuk isyarat berkala masa dískrít di bawah. Plotkan magnitude dan fasa untuk set pekali aK. Determine the Fourier sen'es coeñicients for the following discrete-time periodic signals. Plot the magnitude and phase of the set of coefticients aK. x[n]=1-sinnTTr for0 én SS
4. 4. KEEE 4314/04 x[n] adalah berkala dengan kala 4. x[n] in periodic with period 4. (5 markahlmarks) SOALAN 3/ QUESTION 3 Mempertimbangkan rangkaian sistem LTI yang ditunjuk dalam gambarajah 2 di bawah: Consider the interconnection of LTI systems shown in the following figure 2: x(n) -v ~r y(n) *A (7107) _w I73U7l 7,* (7407) Gambarajah/ Figure 2 (a) Nyatakan sambutan frekuensi sistem keseluruhan dalam sebutan H1(e”^”), Hgüëjw), H3(eI“'), dan H4(e'“'). Express the frequency response of the overall system in terms of H, (e"“'), H2(e"“), H3(e'“), and H4(e'“). (3 markahlmarks) (b) Cari sambutan frekuensi jika Find the frequency response if h1(n) = om) + 2ö(n - 2) + ö(n - 4) h2(n) = ham) = (0.2)” u(n) h4(n) = ö(n _ 2) (9 markahlmarks)
5. 5. KEEE 4314/05 SOALAN 4/ QUESTION 4 (a) Mempertímbangkan satu sistem yang ditakrifkan oleh satu persamaan pembezaan: Consider the system deñned by the difference equation: W? ) = ây(n - 1) + bXUI) + X(n -1) di mana a dan b adalah nyata, dan | a| < 1. Cari hubungan antara a dan b yang mesti wujud jika sambutan frekuensi ini mempunyai magnitude tetap untuk semua w, iaitu, where a and b are real, and ja| < 1. Find the relationship between a and b that must exist if the frequency response is to have a constant magnitude for all w, that is, : H (äwn = 1 (8 markahlmarks) (b) Anggapkan hubungan ini dipatuhi, cari keluaran sistem apabila a = 1/2, dan x(n) = (1l2)” u(n). Assuming that this relationship is satisfied, tind the output of the system when a = 1/2, and x(n) = (1/2)" u(n). (4 markahlmarks) SOALAN 5/ QUESTION 5 Rekabentuk penapis-penapis berikut dengan menggunakan gantian kutub sifar. Design the following tilters by pole-zero placement.
6. 6. KE EE 4314/06 (a) Penapis Iutus jalur dengan frekuensi pusat fo = 200Hz, jalur Iebar 3-dB Af = 20Hz, gandaan sifar pada f = 0Hz dan f = 40OHz, dan frekuensi sampelan pada 80OHz. A bandpass filter with a center frequency of f. , = 200Hz, a 3-dB bandwidth of Af = 20Hz, zero gain at f = O and f = 400Hz and a sampling frequency of 80OHz. (4 markahlmarks) (b) Penapis takuk dengan frekuensi takuk 1kHz, 3-dB jalur batas pada 10 Hz, dan frekuensi sampel pada 8kHz. A notch filter with a notch frequency of 1kHz, a 3-dB stopband of 10Hz, and sampling frequency 8kHz. (4 markahlmarks) (c) Apakah sambutan gandaan untuk penapís takuk pada 45Hz. What is the gain response of this notch filter at 45Hz. (4 markahlmarks) TAMAT END