CENG 420 Design of Digital Signal Processing Systems

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CENG 420 Design of Digital Signal Processing
Systems

• Dr. Brian T. Hemmelman

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Key DSP Operations

• Convolution
• Correlation
• Filtering
• Transformations
• Modulation

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Convolution

• Many uses but a common use is determining a
  systems output if system input and system
  impulse response is known. For continuous system

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Discrete Convolution

• We may however have a computer sampling a signal
  so that we have discrete data.
• So instead of continuous integration process we
  have discrete summation.

• Practically speaking though we would have finite
  sequences x(n) and h(n) of lengths N1 and N2
  respectively, so this is then

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Discrete Convolution

• Note that this is a series of multiplies-followed-
  by-additions, so that this operation is
  fundamentally a Multiply-Accumulate or MAC.
• DSP systems are often benchmarked by the number
  of MACs per second they perform.
• DSP chips (and many FPGAs) have special internal
  architectures that help perform MACs more
  efficiently.

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Correlation

• Correlation is essentially the same as
  convolution (from a computational standpoint).
  You just dont flip anything.
• Instead of describing system output, correlation
  tells us information about the signals.

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Correlation

• Cross-correlation function
• Tells you a measure of similarities between two
  signals.
• Application Identifying radar return signals

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Correlation
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Correlation

• More than one definition of cross-correlation
• One definition for two N-length sequences

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Correlation

• Autocorrelation function
• Correlate a signal with itself.
• Helps find periodicity in signals.

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Correlation
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Digital Filters

• High-pass, low-pass, bandpass, etc.
• Basically same idea as analog filters.
• FIR filter form

• x(n) is input
• y(n) is output
• h(k) are filter coefficients

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Digital Filters
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Discrete Transformations

• Often we want to find the frequency components of
  a signal and/or need to go back and forth between
  the time and frequency domain.
• The most common technique is the DFT (not DTFT)

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Compact Disc Example

• Both channels are sampled and mixed for storage.
• Dual channel data is encoded with a Reed-Solomon
  encoder to fix burst errors (e.g. scratches).
• To be more suitable for optical storage
  Eight-to-Fourteen Modulation (EFM) is used.

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Compact Disc Example

• Optical signal picked off CD and demodulated.
• Reed-Solomon error correction and concealment is
  performed.
• Dual-channel data is oversampled (4x) and split
  into left and right channels.
• Digital data is converted to analog voltage and
  lowpass filtered.

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Fetal ECG Monitoring

• Track babys heart activity through electrical
  potentials on body surface.
• Some key features
• ST segment
• Ratio of T amplitude to QRS amplitude
• Width of QRS complex

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Fetal ECG Monitoring
Cardiotocogram (CTG)
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Fetal ECG Monitoring

• These signals are quite susceptible to noise from
  power supplies, muscle artifacts, poor
  connections, etc.
• Typical approach
• Remove 50/60 Hz noise
• Locate R-wave (most noticeable feature)
• Remove baseline shift
• Filter muscle noise
• Identify ST and PR segments

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Fetal ECG Monitoring
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Signals Review

• Signal A physical quantity that is a function
  of some independent variable such as time or
  space.
• For example

• A is amplitude
• ? is radian frequency (rad/sec)
• ? is phase (rad)

• T is period (sec)
• F is frequency (Hz)

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Signals Review

• Continuous-time signal Function of time that is
  defined for every time instant within a given
  range.
• Continuous function A function differentiable
  everywhere in a given range.
• Continuous-time signals are not necessarily
  continuous functions.

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Signals Review

• Quantized Variable Can only assume values
  from a specified set of numbers. For example, t
  nTs, where n is an integer and Ts is a
  constant.
• Discrete-Time Signal A signal that is quantized
  in time. Usually obtained by sampling.

• Discrete-Time Sequence A discrete-time signal
  without the time reference.

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Digital Signal and Sequence

• Quantized Signal A discrete-time signal with
  quantized amplitude.
• Digital Signal A quantized signal encoded in
  binary.
• Digital Sequence A discrete-time sequence with
  quantized amplitude encoded in binary. Created
  practically by Analog-to-Digital Converter (ADC).
• Quantization can be either magnitude-truncation
  or rounding.
• Distance between two quantization levels is q.

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Quantization
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Sampling Process
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Sampling the Signal
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Holding the Signal
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Quantizing the Signal
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Processing the Signal (Digital Filter)
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Smoothing the Signal (Analog Filter)