DSP_lec1
What is the Signal?
By a signal we mean any variable that carries or contains some kind of information that can be
conveyed, displayed or manipulated.
Definitions of Digital Signal Processing:
Digital: operating by the use of discrete signals to represent data in the form of numbers.
Signal: is any physical quantity that varies with time, space, or any other variable,
A function of independent variables such as time, distance, position, temperature and
pressure, Signals are analog in nature (continuous) such as human voice, electrical signal
(voltage or current), radio wave, optical, audio, and so on which contains a stream of
information or data. Or maybe discrete such as temperature, stock, etc.
Processing: to perform operations on data according to programmed instructions,
Operating in some fashion on signal to extract some useful information.
DSP Applications:
Noise removal from image
Image enhancement
Digital photography
Medicine
Authentication
Continuous-time & discrete-time signal
Continuous-time signal - X(t) Discrete-time signal - X(n)
Time is continuous. Time is discrete.
Signal values are defined for all value of (t). Signal take discrete value (n), n is integer.
Example Example
Volt & current. The result from sampling continuous time
signal.
Analog signal & Digital signal
Analog signal Digital signal
Continuous variable - Continuous amplitude Discrete variables - Discrete amplitude
Time-domain continuous signals. Example
Example Result from quantized discrete-time signals
Speech, Television
Analog signals Digital signal Discrete-time signal
Continuous-amplitude. Discrete-amplitude. Continuous-amplitude.
Continuous-time. Discrete-time. Discrete-time.
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Analog to Digital Converter (ADC)
ADC can be viewed as a three step process.
1-Sampling
Fs=1/Ts is the sampling rate given in samples per second.
Fs>=2Fm to avoid aliasing distortion.
2-Quantization
Quantization: The process of converting discrete-time continuous valued signal into discrete-time discrete
valued (digital) signal
We need to encode each sample value in order to store it in b bits memory location.
But as b is limited, we have to consider a finite values of samples.
For example
o If b = 2, we can have 2^b=4 different possible sample values.
o If b = 4, we can have 2^b=16 different possible sample values.
Important Discrete Time Signals
The basic digital functions (signal or sequence) are
Unit Impulse
Unit Step
Rectangular Signal
Real value exponential
Sinusoidal Signal
Unit Impulse Unit Step Rectangular Signal Real value exponential Sinusoidal Signal
δ[n] U[n]
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Operations on Signals
Signal addition Y (n) = X1(n) + X2(n).
Signal multiplication Y (n) = X1(n) . X2(n).
Scaling Y (n) = a . X1(n).
Shifting 1-unit delay element
Y (n) = X (n-1).
2-unit advance element
Y (n) =X (n+1).
Sample summation
Y (n) = ∑𝑛𝑛=𝑛1 𝑥(𝑛) = 𝑥(𝑛1) + 𝑥(𝑛1 + 1) + … … 𝑥(𝑛)
Sample product
Y (n) = ∏𝑛𝑛=𝑛1 𝑥(𝑛) = 𝑥(𝑛1). 𝑥(𝑛1 + 1) . … … 𝑥(𝑛)
Time reversal
Y (n) = X (-n). Is obtained by reflecting X (n) about n=0.
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Classification of digital signal
Even & Odd Signals
Periodic Signals
Basic System Properties
Memory Causality
System with memory: output value is If the system depend on past input sample
depend on past/future input sample then the system will be causal.
Y (n) =x (n-1)-x^2(n+2). Y (n) =x (n-1).
Memoryless system: output value doesn't If the system depend on future input sample
depend on past/future input sample then the system will be noncausal.
Y (n) =x (n)-x^2(n). Y (n) =x (n+1).
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