PendahuluanAnalisis Spektrum Sinyal Digital

Oleh :Herlan Darmawan

Pendahuluan

• Kontrak kuliah :• 1. absensi : 25%• 2. tugas : 25%• 3. mid : 25%• 4. uas :25%

Pendahuluan

• Why geophysicist/physicist needs to learn “ASSD”?

• What is signal?• What is spectrum?

Why geophysicist needs to learn ASSD

• We deal with geophysical data such as potential field data (gravity, magnetic, or electrical survey).

• That potential data are displayed mostly in 1D (profile form), 2D (map form), or 3D (map and depth display) spatial data.

• When data express thematic value (magnitude vs space /thematic value vs time), it is called time series data or time domain data.

• Time domain data are poor and undiscernable possibly because of noise effects and other measurement errors.

• We need to understand signal processing and signal analysis.

What is signal ??

• A signal is a function of one or more variable as a function of time.

• Signal can be divided :• Continuous-time signal• Discrete-time signal• Periodic signal• Non-periodic signal• Even and odd signal• Exponensial signal

Continuous-time signal

• It is also called an analog signal, defined on the continuum of time values (if the independent variable (t) is continuous) . Example of continuous – time signal :

Discrete-time signal

• A discrete – time signal is defined at discrete times (if the independent variable (t) takes only in discrete values, ex t : ±1, ±2, ±3, etc). It is called a digital signal if its amplitude is quantized to a series of discrete levels.

Discrete time signal Digital signal

Periodic signal

• A continuous – time signal x(t) is periodic with period T, if : x(t+T)=x(t).

• Periodic signal has same wave-shape every T seconds and infinitely often

Non-periodic signal

• Signal that do not repeat at regular intervals

Even and odd signal

• One of the characteristics of signal is symmetry that may be useful for signal analysis. Even signals are symmetric around vertical axis, and odd signal are symmetric about origin.

Exponential signal

• f(t) = 1 (t).A• If α > 0 then is exponentially increasing• If α < 0 then is exponentially decreasing, and• If α = 0 then =1, means the step signal 1(t)

What is spectrum ?

• The spectrum of a signal is a detailed description of the frequency components the signal contains.

• Spectrum analysis also referred to as frequency domain analysis or spectral density estimation.

• The frequency spectrum can be generated via fourier transform.

Introduction to system

• A system is a device which converts an input signal (excitation) into an output signal (response).

• A continuous-time system : input & output are continuous signal

• A discrete-time system : system whose input and output are discrete-time signals.

System classification

• Linear system• When the input is a weighted sum of several inputs,

the output will be the weighted sum of the corresponding inputs. Otherwise, the sistem is nonlinear.

• X1(t) and x2(t) are 2 arbitrary signal, a1 and a2 are two arbitrary constants. System y(t)=T[x(t)] is linear if :

Time-invariant vs time variant systems

• Time invariant system : input signal has a time shift, So the output?. Otherwise, the system is variant

Time shift??

• One of the CT signals operation• Y(t) = x(t-td)• Shift the origin of the signal to td• Ex : y(t) = u(t-2)

Signal operations

• Time reversal y(t) = x(-t)• Time shifting y(t)=x(t-td)• Amplitude scaling y(t) = Bx(t)• Addition y(t)=x1(t) + x2(t)• Multiplication y(t)=x1(t).x2(t)• Time scaling y(t)=x(at)

Time reversal

• Flips the signal about the y axis y(t) = x(-t)• Ex : x(t) = u(t), y(t)=u(-t)• Let “a” be the argument of the step function u(a)

• Let a = -t and plug this value of “a”

Amplitude scaling

• Multiply the entire signal by a constant value• Y(t) = Bx(t)• Sketch y(t)=5u(t)

Addition of signals

• Point-by-point addition of multiple signals• Move from the left to right (/vice versa) and add the value of

each signal together to achieve the final signal• Y(t)=x1(t) + x2(t)• Ex : skecth y(t) = u(t) – u(t-2)• First, plot each of the portions of this signal separately• X1(t) = u(t)• X2(t)=-u(t-1)• Then, move from one side • To other and add their• Instantaneous values

Multiplication of signals

• Point-by-point multiplication of the values• Ex : skecth y(t) = u(t).u(t-2)• Skecth it separately then move from one side

to other, and multiply instantaneous values

Time scaling

• Speed up or slow down a signal• Y(t) = x (at)• |a| > 1 speed up x(t) by factor “a”• |a| < 1 slow down x(t) by factor “a”

• Ex : x(t) = u(t) – u(t-2)• Sketch y(t) = x(2t)• Replace all t’s with 2t• Y(t) = x(2t) = u(2t) – u(2t-2)

• (what occured at t=2 now occurs at t=2/2=1)

First, plot x(t)

Turns on at

No change

Turns on at