Signal Processing Applications in Mechatronics Assist. Prof. Hülya Yalçın e-mail : hulyayalcin@gmail.com Tel : 0212-293-1300 ext:2580 Class hours : Monday 9:30- 12:30 Office hours : Monday 14:30- 16:30 and anytime through email Address : Room 311 in Gümüşsuyu Campus

Signals Hülya Yalçın ©

Continuous-time and discrete-time signals Hülya Yalçın ©

What is a system? Hülya Yalçın ©

Today’s lecture: Hülya Yalçın ©

Linearity Hülya Yalçın ©

Time-invariance Hülya Yalçın ©

Linear time-invariant (LTI) systems Hülya Yalçın ©

Linear System Models - I Hülya Yalçın ©

Linear System Models - II Hülya Yalçın ©

Linear System Models - III Hülya Yalçın ©

Linear System Models - IV Hülya Yalçın ©

Unit Step , Unit Ramp Hülya Yalçın ©

Unit Impulse Hülya Yalçın ©

Main Property of Unit Impulse Hülya Yalçın ©

Transformations of time Hülya Yalçın ©

Examples Hülya Yalçın ©

Shifted Unit Impulse and the Sifting Property Hülya Yalçın ©

Basic Discrete-time Signals Hülya Yalçın ©

Periodic Continuous-time Signals Hülya Yalçın ©

Periodic Discrete-time Signals Hülya Yalçın ©

Next Hülya Yalçın ©

What is a system? Hülya Yalçın ©

Causality Hülya Yalçın ©

Memory Hülya Yalçın ©

Linearity Hülya Yalçın ©

Linearity – example 1 Hülya Yalçın ©

Linearity – example 2 Hülya Yalçın ©

Linearity – example 3 Hülya Yalçın ©

Linearity – example 4 Hülya Yalçın ©

Time - Invariance Hülya Yalçın ©

Time – Invariance : Example 1 Hülya Yalçın ©

Time – Invariance : Example 2 Hülya Yalçın ©

Time – Invariance : Example 3 Hülya Yalçın ©

Linear time-invariant (LTI) systems Hülya Yalçın ©

LTI systems via differential equations Hülya Yalçın ©

The Unit Pulse Response Hülya Yalçın ©

The Unit Pulse Response - continued Hülya Yalçın ©

Convolution Representation Hülya Yalçın ©

Convolution of discrete-time signals Hülya Yalçın ©

Useful properties of Convolution Hülya Yalçın ©

Convolution Representation Hülya Yalçın ©

Computing Discrete Convolution: flip and shift Hülya Yalçın ©

Computing Discrete Convolution: example Hülya Yalçın ©

Computing Discrete Convolution: example cont’ Hülya Yalçın ©

Convolution representation of continuous-time systems Hülya Yalçın ©

The unit impulse response Hülya Yalçın ©

The shifted unit impulse response Hülya Yalçın ©

Derivation of the convolution representation Hülya Yalçın ©

Derivation of the convolution representation Hülya Yalçın ©

Derivation of the convolution representation Hülya Yalçın ©

Convolution of continuous-time signals Hülya Yalçın ©

Additional properties of the convolution Hülya Yalçın ©

Computing convolution integrals: example 1 Hülya Yalçın ©

Computing convolution integrals: example 2 Hülya Yalçın ©

Computing convolution integrals: example 2 Hülya Yalçın ©

Computing convolution integrals: example 2 Hülya Yalçın ©

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Fourier Series Hülya Yalçın ©

Review: vectors Hülya Yalçın ©

Vector Spaces Hülya Yalçın ©

Signal Spaces Hülya Yalçın ©

The space of periodic signals Hülya Yalçın ©

Complete orthonormal sets of functions Hülya Yalçın ©

Fourier Series Hülya Yalçın ©

Fourier Coefficients Hülya Yalçın ©

Convergence of Fourier Series Hülya Yalçın ©

Trigonometric Fourier Series Hülya Yalçın ©

Trigonometric Fourier Series Hülya Yalçın ©

Trigonometric Fourier Series Hülya Yalçın ©

Symmetry Properties Hülya Yalçın ©

Trigonometric Fourier series: example Hülya Yalçın ©

Trigonometric Fourier series: example Hülya Yalçın ©

Complex Exponential Fourier Series Hülya Yalçın ©

Complex Exponential Fourier Series Hülya Yalçın ©

Symmetry Properties for real signals Hülya Yalçın ©

Amplitude and phase spectra Hülya Yalçın ©

Fourier Transform Hülya Yalçın ©

Recap: Fourier Series Hülya Yalçın ©

Spectral content of aperiodic signals: the Fourier transform Hülya Yalçın ©

Example: rectangular pulse Hülya Yalçın ©

Inverse Fourier Transform Hülya Yalçın ©

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Properties of Fourier Transform Hülya Yalçın ©

Properties of Fourier Transform: Linearity Hülya Yalçın ©

Properties of Fourier Transform: Time-shift Hülya Yalçın ©

Multiplication by a complex exponential Multiplication by a cosine Hülya Yalçın ©

Convolution in time-domain Hülya Yalçın ©

Parseval’s Theorem Hülya Yalçın ©

Duality Example Hülya Yalçın ©

Generalized Fourier Transform Hülya Yalçın ©

Fourier Transform of cosine Hülya Yalçın ©

Fourier transform of a periodic signal Hülya Yalçın ©

Bandlimited and timelimited signals Hülya Yalçın ©

Frequency response of LTI systems Hülya Yalçın ©