
Why DSP?
 1. Flexibility in Reconfiguration (Software changes rather than hardware changes).
 2. Controlof accuracy components
 3. More sophisticated algorithims

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*

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.

A random signal is?
A signal that evolves in time in an unpredictable manner.

In discrete time, both omega (w) and frequency (f) have what units?
radians per sample

A D.T. sinusoid can be periodic only if its frequency f is a ______ .
Rational number. > f = k/N (N is the period)

D.T sinusoids whose frequencies are seperated by an interger multiple of _____ are ______.
Identicle

The fundamental range can be expressed as?
\ or

Any 'w' or 'f'' outside the fundamental range is considered what?
A copy or alias.

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.

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,....., N1
 This is the Fourier Series of periodic DT Sequence. It can be represented as
 N1
 x[n] = C_{k}S_{k}[n] where S_{k}[n] = exp(...)
 k=0

The first job of an analogtodigital 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.....

In general, the first step of the analog to digital converter is to what?
x[n] = x _{a}[nT];

The sampling rate can be rate can be represented in what way?
 Sampling Rate = (1/sampling interval) in other words F_{s}= 1/T; where the unit of F_{s }is samples/sec.
 Sampling rate = sampling frequency.

The frequency variable 'f' of the sampled signal can be referred to as what terms?
Relative or normalized frequency

Equations to calculate 'f' of sampled signal
f = F/F _{s }or w = T ( = 2 F)

After the signal is sampled what is the frequency range?
F _{s}/2 F F _{s}/2 _{ }

The Folding frequency can be represent as?
F_{s}/2

The Nyquist rate is what?
 The noaliasing 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
 F_{N}= 2F_{Max}

