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**Jawaharlal Nehru Technological University Anantapur (JNTU) College of Engineering (CEP), Pulivendula, Pulivendula, Andhra Pradesh, India - JNTUACEP**- 5 Topics
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DIGITAL SIGNAL PROCESSING UNIT-1 A signal is defined as any physical quantity that varies with time, space or another independent variable. A system is defined as a physical device that performs an operation on a signal. System is characterized by the type of operation that performs on the signal. Such operations are referred to as signal processing. Advantages of DSP 1. A digital programmable system allows flexibility in reconfi reconfiguring guring the digital signal processing operations by changing the program. In analog redesign of hardware is required. 2. In digital accuracy depends on word length, floating Vs fixed point arithmetic etc. In analog depends on components. 3. Can be stored on disk. 4. It is very difficult to perform precise mathematical operations on signals in analog form but these operations can be routinely implemented on a digital computer using software. 5. Cheaper to implement. 6. Small size. 7. Several filters need several boards in analog, whereas in digital same DSP processor is used for many filters. Disadvantages of DSP 1. When analog signal is changing very fast, it is difficult to convert digital form .(beyond 100KHz range) 2. w=1/2 Sampling rate. 3. Finite word length problems. 4. When the signal is weak, within a few tenths of millivolts, we cannot amplify the signal after it is digitized. 5. DSP hardware is more expensive than general purpose microprocessors & micro controllers. 2 1

6. Dedicated DSP can do better than general purpose DSP. Applications of DSP 1. Filtering. 2. Speech synthesis in which white noise (all frequency components present to the same level) is filtered on a selective frequency basis in order to get an audio signal. 3. Speech compression and expansion for use in radio voice communication. 4. Speech recognition. 5. Signal analysis. 6. Image processing: filtering, edge effects, enhancement. 7. PCM used in telephone communication. 8. High speed MODEM data communication using pulse modulation systems such as FSK, QAM etc. MODEM transmits high speed (1200-19200 bits per second) over a band limited (3-4 KHz) analog telephone wire line. 9. Wave form generation. Classification of Signals I. Based on Variables: 1. f(t)=5t : single variable 2. f(x,y)=2x+3y : two variables 3. S1= A Sin(wt) : real valued signal 4. S2 = A ejwt : A Cos(wt)+j A Sin(wt) : Complex valued signal 5. S4(t)= S 2(t) : Multichannel signal S1(t) S3(t) Ex: due to earth quake, ground acceleration recorder Ir(x, y, t) 6. II. I(x,y,t)= Ig(x, y, t) multidimensional Ib(x, y, t) Based on Representation: 3 2

III. Based on duration. 1. right sided: x(n)=0 for n<N 2. left sided :x(n)=0 for n>N 3. causal : x(n)=0 for n<0 4. Anti causal : x(n)=0 for n ≥ 0 5. Non causal : x(n)=0 for n >N IV. 1. Based on the Shape. δ (n)=0 =1 n=0 2. u (n) =1 n≥ 0 =0 n≠ 0 n<0 Arbitrary sequence can be represented as a sum of scaled, delayed impulses. 4 3

P (n) = a-3 δ (n+3) +a1 δ (u-1) +a2 δ (u-2) +a7 δ (u-7) Or ∞ x(n) = ∑ x(k)δ (n − k) k =−∞ n u(n) = ∑ δ (k) = δ (n) + δ (n-1)+ δ (n-2)….. k =−∞ ∞ = ∑ δ (n − k) k =0 3.Discrete pulse signals. n ≤N Rect (n/2N) =1 else where. =0 5.Tri (n/N) = 1- n /N =0 n ≤N else where. 1. Sinc (n/N)= Sa(n∏ /N) = Sin(n∏ /N) / (n∏ /N), Sinc(0)=1 Sinc (n/N) =0 at n=kN, k= ± 1, ± 2… Sinc (n) = δ (n) for N=1; (Sin (n∏ ) / n ∏ =1= δ (n)) 6.Exponential Sequence x (n) = A α n If A & α are real numbers, then the sequence is real. If 0<α <1 and A is +ve, then sequence values are +ve and decreases with increasing n. For -1<α <0, the sequence values alternate in sign but again decreases in magnitude with increasing n. If α >1, then the sequences grows in magnitude as n increases. 7.Sinusoidal Sequence x(n) = A Cos(won+φ ) for all n 8.Complex exponential sequence 5 4

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