Digital Signal Processing

Rohit Dhongde (B-41)Sushant Burde(B-48)Vaibhav Deshmukh(B-52)Swapnil Dondal (B-49)

What is DSP?Converting a continuously changing waveform

(analog) into a series of discrete levels (digital)

What is DSP?The analog waveform is sliced into equal

segments and the waveform amplitude is measured in the middle of each segment

The collection of measurements make up the digital representation of the waveform

What is DSP?0

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Binary SearchThe speed the binary search is accomplished

depends on:The clock speed of the ADCThe number of bits resolutionCan be shortened by a good guess (but usually is

not worth the effort)

How Does It Work?Faithful Duplication

Now that we can slice up a waveform and convert it into digital form, let’s take a look at how it is used in DSP

Draw a simple waveform on graph paperScale appropriately

“Gather” digital data points to represent the waveform

Starting Waveform Used to Create Digital Data

How Does It Work?Faithful Duplication

Swap your waveform data with a partner

Using the data, recreate the waveform on a sheet of graph paper

Waveform Created from Digital Data

How Does It Work?Faithful Duplication

Compare the original with the recreating, note similarities and differences

How Does It Work?Faithful Duplication

Once the waveform is in digital form, the real power of DSP can be realized by mathematical manipulation of the data

Using EXCEL spreadsheet software can assist in manipulating the data and making graphs quickly

Let’s first do a little filtering of noise

How Does It Work?Faithful Duplication

Using your raw digital data, create a new table of data that averages three data pointsAverage the point before and the point after with

the point in the middleEnter all data in EXCEL to help with graphing

Noise Filtering Using Averaging

Raw

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How Does It Work?Faithful Duplication

Let’s take care of some static crashes that cause some interference

Using your raw digital data, create a new table of data that replaces extreme high and low values:Replace values greater than 100 with 100Replace values less than -100 with -100

ModulationDiscrete signals are rarely transmitted over long distances or stored in large quantities in their raw form.

Signals are normally modulated to match their frequency characteristic to those of the transmission and/or storage media to minimize signal distortion, to utilize the available bandwidth efficiently, or to ensure that the signal have some desirable properties.

Two application areas where the idea of modulation is extensively used are:

1. telecommunications

2. digital audio engineering

High frequency signal is the carrier

The signal we wish to transmit is the modulating signal

Three most commonly used digital modulation schemes for transmitting

Digital data over bandpass channels are:

Amplitude shift keying (ASK)

Phase shift keying (PSK)

Frequency shift keying (FSK)

When digital data is transmitted over an all digital network a scheme known As pulse code modulation (PCM) is used.

Digital Signal Processing And Its

Benefits By a signal we mean any variable that carries or contains some kind of information that can be conveyed, displayed or manipulated.

Examples of signals of particular interest are:

- speech, is encountered in telephony, radio, and everyday life

- biomedical signals, (heart signals, brain signals)

- Sound and music, as reproduced by the compact disc player

- Video and image,

- Radar signals, which are used to determine the range and bearing of distant targets

Attraction of DSP comes from key advantages such as :

* Guaranteed accuracy: (accuracy is only determined by the number of bits used)

* Perfect Reproducibility: Identical performance from unit to unit

ie. A digital recording can be copied or reproduced several times with no

loss in signal quality

* No drift in performance with temperature and age

* Uses advances in semiconductor technology to achieve:

(i) smaller size

(ii) lower cost

(iii) low power consumption

(iv) higher operating speed

* Greater flexibility: Reprogrammable , no need to modify the hardware

* Superior performance

ie. linear phase response can be achieved

complex adaptive filtering becomes possible

Disadvantages of DSP

* Speed and Cost

DSP designs can be expensive, especially when large bandwidth signals

are involved. ADC or DACs are either to expensive or do not have sufficient

resolution for wide bandwidth applications.

* DSP designs can be time consuming plus need the necessary resources

(software etc)

* Finite word-length problems

If only a limited number of bits is used due to economic considerations

serious degradation in system performance may result.

Key DSP Operations1. Convolution

2. Correlation

3. Digital Filtering

4. Discrete Transformation

5. Modulation

Convolution Convolution is one of the most frequently used operations in DSP. Specially in digital filtering applications where two finite and causal sequences x[n] and h[n] of lengths N1 and N2 are convolved

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where, n = 0,1,…….,(M-1) and M = N1 + N2 -1

This is a multiply and accumulate operation and DSP device manufacturers have developed signal processors that perform this action.

Correlation There are two forms of correlation :

1. Auto-correlation

2. Cross-correlation

1. The cross-correlation function (CCF) is a measure of the similarities or shared properties between two signals. Applications are cross-spectral analysis, detection/recovery of signals buried in noise, pattern matching etc.

Given two length-N sequences x[k] and y[k] with zero means, an estimate of their

cross-correlation is given by:

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Where, rxy(n) is an estimate of the cross covarience

The cross-covarience is defined as

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Application AreasImage Processing Instrumentation/Control Speech/Audio Military

Pattern recognition spectrum analysis speech recognition secure communications

Robotic vision noise reduction speech synthesis radar processing

Image enhancement data compression text to speech sonar processing

Facsimile position and rate digital audio missile guidance

animation control equalization

Telecommunications Biomedical Consumer applications

Echo cancellation patient monitoring cellular mobile phones

Adaptive equalization scanners UMTS

ADPCM trans-coders EEG brain mappers digital television

Spread spectrum ECG Analysis digital cameras

Video conferencing X-Ray storage/enhancement internet phone

etc.