Example: dental hygienist

4: Linear Time Invariant Systems

4: Linear Time Invariant Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 1 / 13 LTI Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 LTI Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Com

4: Linear Time Invariant Systems 4: Linear Time Invariant Systems •LTI Systems •Convolution Properties •BIBO Stability •Frequency Response •Causality + •Convolution Complexity •Circular Convolution •Frequency-domain convolution •Overlap Add •Overlap Save •Summary •MATLAB routines DSP and Digital Filters (2017-10159) LTI Systems: 4 – 1 / 13

Fullscreen Download

Information

Domain:

Source:

Link to this page:

Please notify us if you found a problem with this document:

Other abuse

Advertisement

Transcription of 4: Linear Time Invariant Systems

1 4: Linear Time Invariant Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 1 / 13 LTI Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 LTI Systems4.

2 Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 Linear Time- Invariant (LTI) Systems have two properties:LTI Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 Linear Time- Invariant (LTI) Systems have two properties: Linear :H( u[n] + v[n]) = H(u[n]) + H(v[n])LTI Systems4.

3 Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 Linear Time- Invariant (LTI) Systems have two properties: Linear :H( u[n] + v[n]) = H(u[n]) + H(v[n])Time Invariant :y[n] =H(x[n]) y[n r] =H(x[n r]) rLTI Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 Linear Time- Invariant (LTI) Systems have two properties: Linear :H( u[n] + v[n]) = H(u[n]) + H(v[n])Time Invariant :y[n] =H(x[n]) y[n r] =H(x[n r]) rThe behaviour of an LTI system iscompletely defined by its impulseresponse.

4 H[n] =H( [n])LTI Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 Linear Time- Invariant (LTI) Systems have two properties: Linear :H( u[n] + v[n]) = H(u[n]) + H(v[n])Time Invariant :y[n] =H(x[n]) y[n r] =H(x[n r]) rThe behaviour of an LTI system iscompletely defined by its impulseresponse:h[n] =H( [n])Proof:We can always writex[n] = r= x[r] [n r]LTI Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems .

5 4 2 / 13 Linear Time- Invariant (LTI) Systems have two properties: Linear :H( u[n] + v[n]) = H(u[n]) + H(v[n])Time Invariant :y[n] =H(x[n]) y[n r] =H(x[n r]) rThe behaviour of an LTI system iscompletely defined by its impulseresponse:h[n] =H( [n])Proof:We can always writex[n] = r= x[r] [n r]HenceH(x[n]) =H( r= x[r] [n r])LTI Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 Linear Time- Invariant (LTI) Systems have two properties: Linear :H( u[n] + v[n]) = H(u[n]) + H(v[n])Time Invariant :y[n] =H(x[n]) y[n r] =H(x[n r]) rThe behaviour of an LTI system iscompletely defined by its impulseresponse.

6 H[n] =H( [n])Proof:We can always writex[n] = r= x[r] [n r]HenceH(x[n]) =H( r= x[r] [n r])= r= x[r]H( [n r])LTI Systems4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 Linear Time- Invariant (LTI) Systems have two properties: Linear :H( u[n] + v[n]) = H(u[n]) + H(v[n])Time Invariant :y[n] =H(x[n]) y[n r] =H(x[n r]) rThe behaviour of an LTI system iscompletely defined by its impulseresponse:h[n] =H( [n])Proof:We can always writex[n] = r= x[r] [n r]HenceH(x[n]) =H( r= x[r] [n r])= r= x[r]H( [n r])= r= x[r]h[n r]LTI Systems4.

7 Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 2 / 13 Linear Time- Invariant (LTI) Systems have two properties: Linear :H( u[n] + v[n]) = H(u[n]) + H(v[n])Time Invariant :y[n] =H(x[n]) y[n r] =H(x[n r]) rThe behaviour of an LTI system iscompletely defined by its impulseresponse:h[n] =H( [n])Proof:We can always writex[n] = r= x[r] [n r]HenceH(x[n]) =H( r= x[r] [n r])= r= x[r]H( [n r])= r= x[r]h[n r]=x[n] h[n]Convolution Properties4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 3 / 13 Convolution.

8 X[n] v[n] = r= x[r]v[n r]Convolution Properties4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 3 / 13 Convolution:x[n] v[n] = r= x[r]v[n r]Convolution obeysnormal arithmetic rules for multiplication:Convolution Properties4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 3 / 13 Convolution:x[n] v[n] = r= x[r]v[n r]Convolution obeysnormal arithmetic rules for multiplication:Commutative:x[n] v[n] =v[n] x[n]Convolution Properties4.

9 Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 3 / 13 Convolution:x[n] v[n] = r= x[r]v[n r]Convolution obeysnormal arithmetic rules for multiplication:Commutative:x[n] v[n] =v[n] x[n]Proof: rx[r]v[n r](i)= px[n p]v[p](i) substitutep=n rConvolution Properties4: Linear Time InvariantSystems LTI Systems Convolution Properties BIBO Stability Frequency Response Causality+ Convolution Complexity Circular Convolution Frequency-domainconvolution Overlap Add Overlap Save Summary MATLAB routinesDSP and Digital Filters (2017-10159)LTI Systems : 4 3 / 13 Convolution:x[n] v[n] = r= x[r]v[n r]Convolution obeysnormal arithmetic rules for multiplication:Commutat

Show more

Documents from same domain

6: Operational Amplifiers

6: Operational Amplifiers

www.ee.ic.ac.uk

6: Operational Amplifiers 6: Operational Amplifiers •Operational Amplifier •Negative Feedback •Analysing op-amp circuits •Non-inverting amplifier •Voltage Follower

  Operational, Amplifiers, Operational amplifiers, Operational amplifiers 6

FINANCIAL REGULATIONS PREAMBLE

FINANCIAL REGULATIONS PREAMBLE

www.ee.ic.ac.uk

1 FINANCIAL REGULATIONS PREAMBLE 1.1 These Regulations are made by the Director of Finance, acting on the advice of the Management Board, under powers conferred by the Council under paragraph 5 of Ordinance C1.

  Regulations, Financial, Preamble, Financial regulations preamble

Convolution Table (1) Convolution Table (2)

Convolution Table (1) Convolution Table (2)

www.ee.ic.ac.uk

with System’s impulse response h(t). Convolution Integral ... weighted by h(t- τ) (i.e. x(τ) h(t- τ)) for the shaded pulse, PLUS the contribution from all the previous pulses of x(τ). The summation of all these weighted inputs is the convolution integral. L2.4-2 p191

  Convolutions

Signal Transmission through LTI Systems

Signal Transmission through LTI Systems

www.ee.ic.ac.uk

PYKC 20-Feb-11 E2.5 Signals & Linear Systems Lecture 12 Slide 9 Parseval’s Theorem The energy of a signal x(t) can be derived in time or frequency domain:

  Transmissions, Signal, Theorem, Parseval s theorem, Parseval, Signal transmission

Tutorial 7 - Sampling

Tutorial 7 - Sampling

www.ee.ic.ac.uk

PYKC – 11 Feb 08 2 E2.5 Signals & Linear Systems Tutorial Sheet 7 – Sampling (Lectures 12 - 13) 1.* By applying the Parseval’s theorem, show that

  Sampling, Theorem, Parseval s theorem, Parseval, 7 sampling

Lecture 8 - Timing Constraints

Lecture 8 - Timing Constraints

www.ee.ic.ac.uk

Metastability is a problem that arises when an external input NOT synchronised to the system clock is fed into our synchronous circuit. Since the input signal could change anytime relative the the clock edge, metastability will occur. It could also happens when a signal crosses from one clock domain (Clock1) to another clock domain (Clock2).

  Metastability

14: Power in AC Circuits

14: Power in AC Circuits

www.ee.ic.ac.uk

Cosine Wave RMS 14: Power in AC Circuits •Average Power •Cosine Wave RMS •Power Factor + •Complex Power •Power in R, L, C •Tellegen’s Theorem •Power Factor Correction •Ideal Transformer •Transformer Applications •Summary E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 3 / 11 Cosine Wave: v(t) = 5cosωt.Amplitude is V = 5V. Squared Voltage: v2(t) = …

SERVO MOTOR SG90 DATA SHEET - Imperial College London

SERVO MOTOR SG90 DATA SHEET - Imperial College London

www.ee.ic.ac.uk

SERVO MOTOR SG90 DATA SHEET Tiny and lightweight with high output power. Servo can rotate approximately 180 degrees (90 in each direction), and works just like the standard kinds but smaller. You can use any servo code, hardware or library to control these servos.

  Sheet, Data, Motor, Data sheet, Servo, Servo motors

17: Transmission Lines

17: Transmission Lines

www.ee.ic.ac.uk

• Forward Wave • Forward ... A transmission line is a wire with a uniform goemetry along its length: the capacitance and inductance of any segment is proportional to its length. We represent as a large number of small inductors and capacitors spaced along the line.

  Waves, Length

8: Correlation - Imperial College London

8: Correlation - Imperial College London

www.ee.ic.ac.uk

E1.10 Fourier Series and Transforms (2015-5585) Fourier Transform - Correlation: 8 – 3 / 11 Cross correlation is used to find where two signals match: u(t) is the test waveform.

  Tests, Correlations

Related documents

The IC Diet

The IC Diet

www.ic-diet.com

Sep 18, 2009 · Interstitial Cystitis Association (www.ichelp.org) Beverley Laumann, Author, Support Group Leader A Taste of the Good Life: A Cookbook for an IC Diet Fresh Tastes by Bev – IC diet column Jill Osborne MA, Author & President Interstitial Cystitis Network (www.ic-network.com) Barbara Shorter, EdD, RD, CDN

  Diet, Interstitial, Cystitis, The ic diet, Interstitial cystitis

Future Technology Devices International Ltd

Future Technology Devices International Ltd

www.ftdichip.com

UART/FIFO IC Datasheet Version 2.0 Document No.: FT_000288 Clearance No.: FTDI #199 Future Technology Devices International Ltd FT232H Single Channel Hi-Speed USB to Multipurpose UART/FIFO IC The FT232H is a single channel USB 2.0 Hi-Speed (480Mb/s) to UART/FIFO IC. It has the capability of being configured in a variety of industry standard

IC SCH PRINTABLE MAY QUALS 20211008

IC SCH PRINTABLE MAY QUALS 20211008

www.indycar.com

IC_SCH_PRINTABLE_MAY_QUALS_20211008 Created Date: 10/8/2021 12:13:30 PM ...

MAX3222/MAX3232/MAX3237/MAX3241 - 3.0V to 5.5V, Low …

MAX3222/MAX3232/MAX3237/MAX3241 - 3.0V to 5.5V, Low …

datasheets.maximintegrated.com

(VCC = +3.0V to +5.5V, C1–C4 = 0.1μF (Note 2), TA = TMIN to TMAX, unless otherwise noted. Typical values are at TA = +25°C.) Note 2: MAX3222/MAX3232/MAX3241: C1–C4 = 0.1μF tested at 3.3V ±10%; C1 = 0.047μF, C2–C4 = 0.33μF tested at 5.0V ±10%. MAX3237: C1–C4 = 0.1μF tested at 3.3V ±5%; C1–C4 = 0.22μF tested at 3.3V ±10%; C1 = 0.047μF, C2–C4 = 0.33μF

Inductor Calculation for Buck Converter IC

Inductor Calculation for Buck Converter IC

fscdn.rohm.com

Switching Regulator IC Series Inductor Calculation for Buck Converter IC This application note covers the steps required in choosing the inductor and to calculate the value used in buck regulator IC circuits. Buck (Step-Down) Converter Switching regulators are used in a variety of applications to provide stable and efficient power conversion.

  Converter, Buck, Buck converter ic

IC 35-38-9 Chapter 9. Sealing and Expunging Conviction ...

IC 35-38-9 Chapter 9. Sealing and Expunging Conviction ...

www.in.gov

IC 35-38-9 Chapter 9. Sealing and Expunging Conviction Records IC 35-38-9-1 Expunging arrest records Sec. 1. (a) This section applies only to a person who has been arrested, charged with an offense, or alleged to be a delinquent child, if: (1) the arrest, criminal charge, or juvenile delinquency allegation:

µA741 General-Purpose Operational Amplifiers

µA741 General-Purpose Operational Amplifiers

www.ti.com

(1) For more information about traditional and new thermal metrics, see the Semiconductor and IC Package Thermal Metrics application report. 6.3 Thermal Information THERMAL METRIC(1) µA741 D (SOIC) P (PDIP) PS (SO) UNIT 8 PINS 8 PINS 8 PINS RθJA Junction-to-ambient thermal resistance 129.2 87.4 119.7 °C/W

Related search queries

The IC Diet, Interstitial Cystitis, Buck Converter IC, Converter