Ch.3 Analog-to-Digital Signal Conversion

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Ch.3 Analog-to-Digital Signal Conversion

• DSP-LabVIEW

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Lab 3 Sampling, Quantization, and
ReconstructionL3.1Aliasing

• Assume that no band-limiting filter is applied
  before a signal is sampled.
• Then, there is the possibility of aliasing.
• Let a signal be sampled at fs Hz.
• Let the frequency of an input signal be f.
• The normalized frequency is f/fswhen this value
  is larger than .5, then aliasing occurs.

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L3.1 Aliasing (p.2)

• Sampling of a sinusoidal signal
• fs 1 k Hz
• Number of samples N 10
• Time between samples, Ts 1/fs .001 sec
• Time for N samples Ts x N 10 x .00110ms
• If f 300 Hz, then 300/1,000 .3 lt.5
• No aliasing.
• If f 700 Hz, then 700/1,000 .7 gt .5
• Aliasing--the samples look like they came from a
  300 Hz signal.
• In the discrete simulation, the analog signal is
  implemented by oversampling.

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L3.2 Fast Fourier Transform

• Recall Equation 3.6, page 62
• Let f be the frequency of a sinusoid.
• Let m be the number of cycles of a sinusoid, over
  which a DFT is computed.
• Let N be the number of samples of the sinusoid in
  the computation.
• Let fs be the sampling frequency.
• Then f (m/N)fs is the condition for an
  undistorted DFT computation.

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L3.2 FFT (p.2)

• Express VIs are used for simulating signals at
  250Hz and 251 Hz.
• Express VIs are also used for spectrum analysis
  (using FFT computations).
• For the 251 Hz signal, the energy is spread over
  a wider frequency ranged and the peak is 4dB down.

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L3.3 Quantization

• A signal is generated using the following
  formula
• y(t) 5.2 exp (-10t)sin(20?t) 2.5 (page 80)
• The signal has the following characteristics
• Value at t0 is 2.5 (DC offset)
• Sinusoidal waveform with exponential decreasing
  amplitude.
• Max is 7 and minimum is 0.
• As t gets large, y(t) tends to 2.5
• 3 bits can be used for quantization, (0 to 7
  values).

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L3.3 Quantization (p.2)

• A Formula Waveform VI is used to generated the
  original signal.
• The quantization process is simulated using
• Numeric conversion of a double precision value to
  an unsigned integer.
• Using the Build Waveform function to construct
  the quantized waveform from the unsigned (byte)
  integer values.

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L3.3 Quantization (p.3)

• Quantization Error
• The difference between the original signal and
  the quantized signal.
• E(t) Yq(t) Y(t)
• Displays
• The original signal and the quantized signal.
• The quantization error.
• The histogram of the error.

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L3.4 Signal Reconstruction

• A signal is sampled and then reconstructed using
  the convolution (interpolation) equation, Eq.
  3.7.
• The interpolation function is a sinc function.
• Oversampling is simulated using zero insertion.
• The sinc function is truncated, using a specified
  number of zero crossings.