All that I have studied till now


  • There are two kinds of Analog signals: Continuous and Discrete
  • What is Sample & Hold?
When in a discrete signalling, the value of signal is selected after each interval of time, then that interval of time is known as sampling interval. And such a circuit which enables us to do so is called the Sample and hold circuit.
  • We are getting the value of the signal at every interval, which is integral multiple of sampling interval (T).
  • A digital signal is discrete in space as well as time.-Quantization: Discreetness in Amplitude as well as Time.
  • Hence, every continuous time signal is an analog signal but every analog signal is not continuous time signal.
  • We need to remove abrupt change and to remove them we need to improve the higher frequencies (which have infinite harmonics). That is why we pass it through low pass filter.
  • Advantages of DSP
    1. Less Sensitivity: In case of analog, noise remains in the signal but in digital, it is less sensitive. For eg. if V=5V and 10% error (or noise) then in
      1. analog: 4.5 and 5.5 is Vmax
      2. digital: 4.5 and 5.5 but always represented by 1 as it is approximated to 5V which is taken to be 1.
    2. Volume Production: Tuning is not needed in digital signalling (opposite of analog- like its needed in radios).
    3. Integration of Circuits: Analog has inductors (which are impossible to minimize and are costly) whereas in Digital, there is no use of inductors
    4. Accuracy increases as the word length increases: in digital 4.2,4,4.212.4.12121 are all 4
    5. Dynamic range increases with floating point: Any length of data can be used for eg 5V can be 5000 and -5 as -5000.
    6. Time sharing of processor: Digital processor is multitasking (simultaneous tasking)
    7. Multirate processing: Sampling rates may be different in digital
    8. Easy storage
    9. Very low frequency processing: At low frequency inductance creates problems in analog which is not the thing in digital.
  • Disadvantages of DSP
    1. Complexity increases
    2. Power dissipation in CMOS
    3. frequency range is limited (because of the 'T' of the sample and hold circuit which can not be decreased to 0 to make the frequency infinite).
Let xa (t)= Acos(wt+phi)
let T be the sampling time interval, so T=1/Fs (which is sampling frequency)
so x(n)=Acos(wnT+phi)
and w=2*pi*F
so x(n)=Acos(2*pi*F*n*T+phi)
now as, T=1/Fs so, x(n)=Acos(2*pi*F*n*1/Fs+phi)= Acos(2*pi*f*n+phi)
Here f=F/Fs (normalized frequency)

 Sampling Theorem: Fs>=2Fm
Fm is obtained from, w=2*pi*Fm
Sampling frequency should be more than twice the Maximum Frequency
Minimum Fs that can be used is 2Fm
  • Why should minimum Fs be 2Fm or more than that?
  • When Fs=2*Fmax
  • and f=Fmax/Fs so the maximum f can be 1/2 so w (=2*pi*f)=pi
  • For analog frequency is between -inf to +inf but in digital frequency is between -1/2 to 1/2.

  1. f=F/Fs
  2. Multiplying 2pi both the sides, 2*pi*f= 2*pi*F/Fs (f is discrete frequency and F is analog frequency)
  3. This equation can be written as, w= (W)/Fs (w=sampled omega, W= complete omega)
  4. w=radian/sample and W=radian/sec
  5. Now for discrete signal, f is between +-1/2 and w is between +-pi.
  • Difference between Continuous Time SIgnal and Discrete Time Signal
    • Continuous Time Signal:
      • W=2*pi*F
      • rad/s
      • F=Analog Frequency (Hz)
      • Range:
        • -inf<=W<=+inf
        • -inf<=F<=+inf
  • Continuous Time Signal:
      • W=2*pi*f
      • rad/sample
      • F=Normalized Frequency (cycles/sample)
      • Range:
        • -pi<=w<=+pi
        • -1/2<=f<=+1/2

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