Digital Signal Processing:

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Digital Signal Processing: Mathematical and algorithmic manipulation of discretized and quantized or naturally digital signals in order to extract the most

1 Digital Signal Processing: Mathematical and algorithmic manipulation of discretized and quantized or naturally digital signals in order to extract the most relevant and pertinent information that is carried by the signal. What is a signal? What is a system? What is processing? Applied Signal Processing - Lecture 1

2 Examples of signals: Applied Signal Processing - Lecture 1

3 Characterization of signals: Continuous time signals vs. discrete time signals e.g. Temperature in the building at any time Continuous valued signals vs. digital signals e.g. Amount of current drawn by a device; average exam grades - Continuous time and continuous valued: Analog signal - Continuous time and discrete valued: Quantized signal - Discrete time and continuous valued: Sampled signal - Discrete time and discrete values: Digital signal (CD audio) Real-valued signals vs. complex-valued signals Single channel vs. multi-channel signals e.g. Blood pressure signal 128 channel EEG Deterministic vs. random signal One-dimensional vs. two-dimensional vs. multi-dimensional signals Applied Signal Processing - Lecture 1

4 Applied Signal Processing - Lecture 1

5 - Any physical quantity that is represented as a function of an independent variable is called a signal. independent varables can be time, frequency, space etc. - Every signal carries information. However, not all that information is typically of interest to the user. The goal of signal processing is to extract the useful information from the signal - The part of the signal that is not useful is called noise. Noise is not necessarily noisy. Any part of the signal we are not interested in is by definition noise. Applied Signal Processing - Lecture 1

6 Applied Signal Processing - Lecture 1

7 Sinusoids play a very important role in signal processing, because They are easy to generate They are easy to work with; their mathematical properties are well known Most importantly: all signals can be written as a sum of sinusoids, through Fourier transforms (later). In continuous time: Applied Signal Processing - Lecture 1

8 - A discrete-time signal, commonly referred to as a sequence, is only defined at discrete time instances, where t is defined to take integer values only. - Discrete-time signals may also be written as a sequence of numbers inside braces: {x[n]} = {..., -0.2, 2.2, 1.1, 0.2, -3.7, 2.9,...} n indicates discrete time, in integer intervals, the bold-face number is at t = 0. Applied Signal Processing - Lecture 1

9 - Discrete-time signals are often generated from continuous time signals by sampling, which can roughly be interpreted as quantizing the independent variable (time). {x[n]} = x(nt S ) = x( t ) t=nts n =...,-2,-1,0,1,2,... T S = Sampling interval/period f S = 1/T S = Sampling frequency Applied Signal Processing - Lecture 1

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14 ZERO ORDER HOLD Applied Signal Processing - Lecture 1

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21 Examples of filtering Applied Signal Processing - Lecture 1

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23 Analysis of ECG Signals Applied Signal Processing - Lecture 1

Depending on the material in the soil the

24 Analysis of seismic waves: study the structure of the soil by analyzing seismic waves, wither natural (earthquakes, volcanic eruptions) or man-made (explosions etc.) Useful e.g. for exploration of oil. Depending on the material in the soil the reflected waves have different frequencies (modes). Applied Signal Processing - Lecture 1

25 travel time Seismic signals as a function of position Applied Signal Processing - Lecture 1

26 Dolby Noise Reduction Scheme A Compressor Applied Signal Processing - Lecture 1

27 Dolby Noise Reduction Scheme Applied Signal Processing - Lecture 1

28 Applied Signal Processing - Lecture 1

34 Î¼n 1 n 0 Î¼n 0 n< 0

43 [ ] [ ] [ n] x n=x n+x ev od [ ] [ ] [ ] x n=x n+x n cs ca

44 E = x n= [ ] ( x n ) 2

46 1 1 N n= 0 ( [ ]) P= x xn N 2

49 bounded summable square summable

Digital Signal Processing Lecture 1

Remote Sensing Laboratory Dept. of Information Engineering and Computer Science University of Trento Via Sommarive, 14, I-38123 Povo, Trento, Italy Digital Signal Processing Lecture 1 Prof. Begüm Demir