EEE 420 Digital Signal Processing Instructor Erhan A

EEE 420 Digital Signal Processing Instructor : Erhan A. Ince E-mail: erhan. ince@emu. edu. tr Web page address: http: //faraday. ee. emu. edu. tr/eeng 420

Digital Signal Processing And Its Benefits By a signal we mean any variable that carries or contains some kind of information that can be conveyed, displayed or manipulated. Examples of signals of particular interest are: - speech, is encountered in telephony, radio, and everyday life - biomedical signals, (heart signals, brain signals) - Sound and music, as reproduced by the compact disc player - Video and image, - Radar signals, which are used to determine the range and bearing of distant targets

Attraction of DSP comes from key advantages such as : * Guaranteed accuracy: (accuracy is only determined by the number of bits used) * Perfect Reproducibility: Identical performance from unit to unit ie. A digital recording can be copied or reproduced several times with no loss in signal quality * No drift in performance with temperature and age * Uses advances in semiconductor technology to achieve: (i) smaller size (ii) lower cost (iii) low power consumption (iv) higher operating speed * Greater flexibility: Reprogrammable , no need to modify the hardware * Superior performance ie. linear phase response can be achieved complex adaptive filtering becomes possible

Disadvantages of DSP * Speed and Cost DSP designs can be expensive, especially when large bandwidth signals are involved. ADC or DACs are either to expensive or do not have sufficient resolution for wide bandwidth applications. * DSP designs can be time consuming plus need the necessary resources (software etc) * Finite word-length problems If only a limited number of bits is used due to economic considerations serious degradation in system performance may result.

Application Areas Image Processing Instrumentation/Control Pattern recognition spectrum analysis Robotic vision noise reduction Image enhancement data compression Facsimile position and rate animation control Telecommunications Echo cancellation Adaptive equalization ADPCM trans-coders Spread spectrum Video conferencing Speech/Audio speech recognition speech synthesis text to speech digital audio equalization Biomedical patient monitoring scanners EEG brain mappers ECG Analysis X-Ray storage/enhancement Military secure communications radar processing sonar processing missile guidance Consumer applications cellular mobile phones UMTS digital television digital cameras internet phone etc.

Key DSP Operations 1. 2. 3. 4. 5. Convolution Correlation Digital Filtering Discrete Transformation Modulation

Convolution is one of the most frequently used operations in DSP. Specially in digital filtering applications where two finite and causal sequences x[n] and h[n] of lengths N 1 and N 2 are convolved where, n = 0, 1, ……. , (M-1) and M = N 1 + N 2 -1 This is a multiply and accumulate operation and DSP device manufacturers have developed signal processors that perform this action.

Correlation There are two forms of correlation : 1. Auto-correlation 2. Cross-correlation 1. The cross-correlation function (CCF) is a measure of the similarities or shared properties between two signals. Applications are cross-spectral analysis, detection/recovery of signals buried in noise, pattern matching etc. Given two length-N sequences x[k] and y[k] with zero means, an estimate of their cross-correlation is given by: Where, rxy(n) is an estimate of the cross covarience

The cross-covarience is defined as

2. An estimate of the auto-correlation with zero mean is given by of an length-N sequence x[k]

Digital Filtering The equation for finite impulse response (FIR) filtering is Where, x[k] and y[k] are the input and output of the filter respectively and h[k] for k = 0, 1, 2, ………, N-1 are the filter coefficients

Filter structure A common filtering objective is to remove or reduce noise from a wanted signal.

(a) (d) (b) (e) (c) (f) Figure : Reconstructed bi-level text images for degradation caused by h 1 and AWGN. (a) Original, (b) 2 D Inverse, (c) 2 D Wiener, (d)PIDD, (e) 2 D VA-DF, (f) PEB-FCNRT

Discrete Transformation Discrete transforms allow the representation of discrete-time signals in the frequency domain or the conversion between time and frequency domain representations. Many discrete transformations exists but the discrete Fourier transform (DFT) is the most widely used one. DFT is defined as: IDFT is defined as:

MATLAB function for DFT function [Xk] = dft(xn) N=length(xn); n = 0: 1: N-1; % row vector for n k = 0: 1: N-1; % row vecor for k WN = exp(-1 j*2*pi/N); % Twiddle factor (w) nk = n'*k; % creates a N by N matrix of nk values WNnk = WN. ^ nk; % DFT matrix Xk = (WNnk*xn' );

Matlab Function for IDFT function [xn] = idft(Xk) % Computes Inverse Discrete Transform % -----------------% [xn] = idft(Xk) % xn = N-point sequence over 0 <= n <= N-1 % Xk = DFT coeff. array over 0 <= k <= N-1 % N = length of DFT % N = length(Xk); n = [0: 1: N-1]; k = [0: 1: N-1]; WN = exp(-j*2*pi/N); nk = n'*k; WNnk = WN. ^ (-nk); xn = (Xk' * WNnk)/N; % row vector for n % row vecor for k % Wn factor % N by N matrix of nk values % IDFT matrix % row vector for IDFT values

Example Let x[n] be a 4 -point sequence >>x=[1, 1, 1, 1]; >>N = 4; >>X = dft(x, N); >>mag. X = abs(X) ; >>pha. X = angle(X) * 180/pi; mag. X= 4. 0000 0 -134. 981 -90. 00 -44. 997 pha. X=

Modulation Discrete signals are rarely transmitted over long distances or stored in large quantities in their raw form. Signals are normally modulated to match their frequency characteristic to those of the transmission and/or storage media to minimize signal distortion, to utilize the available bandwidth efficiently, or to ensure that the signal have some desirable properties. Two application areas where the idea of modulation is extensively used are: 1. telecommunications 2. digital audio engineering High frequency signal is the carrier The signal we wish to transmit is the modulating signal

Three most commonly used digital modulation schemes for transmitting Digital data over bandpass channels are: Amplitude shift keying (ASK) Phase shift keying (PSK) Frequency shift keying (FSK) When digital data is transmitted over an all digital network a scheme known As pulse code modulation (PCM) is used.