Exam - Signal Spectra and Signal Processing (SSPL01E) Digital Signal Processing (SSPL01E)

What do these images have in common?

What’s in it for me?

Any physical quantity that varies with time, space or any other independent variable or variables

Mathematically described as a function of one or more independent variables

Equation for Varies Linearly with Time?

Equation for Varies Quadratically with Time?

Equation for Two independent variables (x,y) as spatial coordinates in a plane?

Most of the Signals in Science and Engineering are Analog and can be processed directly by appropriate Analog Systems. Examples are?

Digital Signal Processing is Widely Used due to its advantages:

Classifications of Signals. Signals Generated from Multiple Sources or Multiple Sensors Examples is ECG (Electrocardiograms) 3 leads or 12 leads

Classifications of Signals. Signals Generated from Multiple Independent Variables Example is Black and White TV > Intensity and Brightness as a function of Time

What classification of signal is this?

Colored TV is considered as?

Is the brightness of Red, Green, and Blue as a function of time

Classification of Signals. • “Analog Signals” • Defined for every single value of time • Take values on continuous interval.

Classification of Signals. • Defined on certain specific values of time • Not required, but in practice, are done equidistant

Classification of Signals. Signal takes all the possible values on the infinite or finite range

Classification of Signals. • “Digital Signal” • Signal takes values from a finite set of possible values

Classification of Signals. • Can be described by explicit mathematical expression, table of data, well-defined rule • All values of signal (past, present, future) are known precisely, without uncertainty

Classification of Signals. • Cannot be descrived by any reasonable degree of accuracy by explicit mathematical formulas, or too complicated for any practical use

Applications of DSP to the Real World. Digital audio coding such as CD players and MP3 players, digital crossover, digital audio equalizers, digital stereo and surround sound, noise reduction systems, speech coding, data compression and encryption, speech synthesis and speech recognition

Speech recognition, high-speed modems, echo cancellation, speech synthesizers, DTMF (dual-tone multifrequency) generation and detection, answering machines

Active noise control systems, active suspension systems, digital audio and radio, digital controls, vibration signal analysis

Cellular phones, digital telecommunications, wireless LAN (local area networking), satellite communications

ECG analyzers, cardiac monitoring, medical imaging and image recognition, digital X-rays and image processing

Internet phones, audio and video, hard disk drive electronics, iPhone, iPad, digital pictures, digital cameras, text-to-voice and voice-to-text technologies

Applications of DSP to the Real World

DSP Application in the Real World.

> Continuous signal in both Time and Amplitude > Current, Voltage, Temperature, Pressure, Light Intensity, and so on.

> Contains the digital values converted from the analog signal at the specified time instants > Can be manipulated using arithmetic. Manipulations include digital filtering, and the likes > Can be converted back to an analog signal by sending the digital values to DAC to produce the corresponding voltage levels and applying a smooth filter (reconstruction filter) to the DAC voltage steps.

What type of time signal is this?

Is a indexed sequence of real or complex numbers

Function of an integer-valued variable, n, that is denoted by x(n)

• Often derived by sampling a continuous-time signal with an ADC > Sample for a continuous-time signal x(t) that is sampled at a rate of Fs = l/Ts samples per second produces the sampled signal x(n), which is related to xa(t) as follows

Other Representations of Discrete Time Signals

• Unit Sample Sequence - δ(n)

> Signal is Zero everywhere except n=0 > Also called “unit impulse”

> Signal is Zero when n<0

> Signal is linearly proportional to n when n ≠ 0

What Exponential Signal is this?

Type of Elementary Discrete Signal

What Exponential Signal is this?

Classification of Discrete Time Signals. Sequence repeats itself every period (N)

Classification of Discrete Time Signals. Does not meet above criteria

Classification of Discrete Time Signals.An x1 (n) with a period of N1 , plus x2 (n) with a period of N2 What is the period of

Classification of Discrete Time Signals: 𝑥 𝑛 = 𝑥(−𝑛)

Classification of Discrete Time Signals: 𝑥 𝑛 = −𝑥(−𝑛)S

Time Manipulation (delaying/advancing) - Shifting. A signal x(n) may be shifted in time by replacing the independent variable (n) by (n-k); k is an _________.

Delay the signal by k units in time

Advances the signal by |k| units in time

� A signal x(n) may be shifted in time by replacing the independent variable (n) by (n-k); k is an integer • +k delay the signal by k units in time • -k advances the signal by |k| units in time • Example: x(n)

• Replacing n by –n; reflection at time origin n=0 • Example: x(n)

� Replacing n by µn; reflection at time origin n=0 • Taking every µ sample • Example: x(n)

Of a signal is accomplished by multiplying the value of every signal by sample A

Of two signals x1(n) and x2(n) whose value at any instant is equal to the sum of the values for that instant

Of two signals x1(n) and x2(n) whose value at any instant is equal to the product of the values for that instant

Examples of Amplitude Scaling, Addition, & Multiplication

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