D R . T A R E K T U T U N J I
P H I L A D E L P H I A U N I V E R S I T Y , J O R D A N
2 0 1 4
Analog to Digital Conversion
Analog to Digital Conversion
Sampling
The Conversion of a continuous-time signal into a discrete-time signal obtained by taking samples of the continuous-time signal at discrete-time instants
Quantization
The conversion of a discrete-time continuous-valued signal into a discrete-time, discrete-valued signal (i.e. digital signal)
Coding
Each discrete value is represented by a binary sequence
Sinusoidal Example: Sampling
Suppose x(t) = 5 cos (2pft) where f=10KHz
Find the discrete-time signal x(n) when sampling frequency is
fs = 50 KHz
fs = 100 KHz
Aliasing
Aliasing refers to an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled.
Anti Aliasing Filter
An anti-aliasing filter is a filter used before a signal sampler, to restrict the bandwidth of a signal to approximately satisfy the sampling theorem
Sinusoidal Example: Quantization
Recall the signal x(t) = 5 cos (2pft) where f=10KHz
The sampled signal x(n) with fs =100 KHz was provided: [5, 4.05, 1.55, -1.55, -4.05, -5, -4.05, -1.55, 1.55, 4.05]
8-level quantization is used with range of 10 volts
Draw the xQ(n) signal
Provide the coding result
Basic Components of DSP Systems
1. A lowpass analog antialiasing pre-filter that bandlimits the signal to be sampled to within the Nyquist interval.
2. An A/D converter (sampler and quantizer).
3. A digital signal processor.
4. A D/A converter (staircase reconstructor), possibly preceded by an equalizing digital filter.
5. A lowpass analog anti-image postfilter to complete the job of the staircase reconstructor and further remove the spectral images introduced by the sampling process.
Conclusion
Analog to Digital operation involves the following stages: Sampling
Quantization
Coding
The sampling frequency should be at least larger than two times maximum frequency in the signals
Digital to Analog operation tries to reconstruct the analog signal using ZOH