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Why DSP?
- 1. Flexibility in Reconfiguration (Software changes rather than hardware changes).
- 2. Controlof accuracy components
- 3. More sophisticated algorithims
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Quantization can be performed in two ways. Those ways are?
- 1. Rounding (8.58 --> 9)
- 2. Truncation (8.68 -->8)
*Introduce error at this point*
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A deterministic signal is?
A signal that can be uniquely described by an explict mathmatical expression, a table or data or a well defined rule.
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A random signal is?
A signal that evolves in time in an unpredictable manner.
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In discrete time, both omega (w) and frequency (f) have what units?
radians per sample
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A D.T. sinusoid can be periodic only if its frequency f is a ______ .
Rational number. ---> f = k/N (N is the period)
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D.T sinusoids whose frequencies are seperated by an interger multiple of _____ are ______.
 Identicle
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The fundamental range can be expressed as?
\ or
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Any 'w' or 'f'' outside the fundamental range is considered what?
A copy or alias.
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What is the purpose of the Fourier Series?
To take complicated systems, break them down to simpilier, easier to work with signal that can be manipulated mathmatically.
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If N = 3 we can choose {s 0[n], s 1[n], s 2[n] } all of which are unique. In General we can choose {s k[n]} -->( k th Harmonic of x[n]]} = to for k = 0,1,2,....., N-1
- This is the Fourier Series of periodic DT Sequence. It can be represented as
- N-1
- x[n] = CkSk[n] where Sk[n] = exp(...)
- k=0
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The first job of an analog-to-digital converter (ADC) is to what?
- It is to sample the analog signal at discrete time instants.
- -If the sampling interval is 'T' seconds then samples will be taken every 'nT' seconds. Where n = 0,1,2,3.....
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In general, the first step of the analog to digital converter is to what?
x[n] = x a[nT];
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The sampling rate can be rate can be represented in what way?
- Sampling Rate = (1/sampling interval) in other words Fs= 1/T; where the unit of Fs is samples/sec.
- Sampling rate = sampling frequency.
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The frequency variable 'f' of the sampled signal can be referred to as what terms?
Relative or normalized frequency
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Equations to calculate 'f' of sampled signal
f = F/F s or w = T ( = 2 F)
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After the signal is sampled what is the frequency range?
-F s/2 F F s/2
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The Folding frequency can be represent as?
Fs/2
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The Nyquist rate is what?
- The no-aliasing condition. It is the sampling rate that allows for the original analog signal to be reconstructed from the D.T signal. It is given by
- FN= 2FMax
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