# Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #10 Signal Analysis & Processing – Frequency Response & Filters Dr. Han Le ECE Dept.

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Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #10 Signal Analysis & Processing – Frequency Response & Filters Dr. Han Le ECE Dept.

Han Q Le© Outline Review Signal analysis – Power spectral density Frequency response of a system (circuit) – Transfer function – Bode plot Filters – Analog – Digital

Han Q Le© Concept Review: Signal Processing All electronics around us involve signal processing. Signal represents information. That information can be something we generate (e.g. texts, sounds, music, images) or from sensors. (discussion: examples of sensors) Electronics deal with signals: signal processing is to transform the signal and extract the desired information.

Han Q Le© Concept Review: Signal Processing (cont.) Signal processing is a general concept, not a single specific thing. It includes: – signal synthesis or signal acquisition – signal conditioning (transforming): shaping, filtering, amplifying – signal transmitting – signal receiving and analysis: transforming the signal, converting into information Signal processing is mathematical operation; electronics are simply tools. Computation is high-level signal processing: dealing directly with information rather than signal.

Han Q Le© Applications of mathematical techniques Fourier transform Harmonic function Complex number &analysis Phasors Signal and AC circuit problems RLC or any time-varying linear circuits. Applicable to linear portion of circuits that include nonlinear elements Signal processing signal analysis (spectral decomposition) filtering, conditioning (inc amplification) synthesizing Note: The main lecture material is in the Mathematica file – this is only for concept summary

Han Q Le© Homework (to be seen in HW 8) Choose an electronic system around you (e. g. a TV, DVD player, phone,…); show a functional block diagram and describe the signal processing sequence (end to end).

Han Q Le© Example Antenna Ground Inductor Variable Capacitor Diode (1N34A) High-Impedance Earphone

Han Q Le© Schematic Ante nna Grou nd Inductor Variable Capacitor Diode (1N34A) High-Impedance Earphone SoundwaveElectrical signal (voltage or current) Antenna Carrier wave (sound) signal Resonance circuit

Han Q Le© Outline Review Signal analysis – Power spectral density Frequency response of a system (circuit) – Transfer function – Bode plot Filters – Analog – Digital

Han Q Le© Signal Fourier (or harmonic) Analysis Treat each time-finite signal as if it is composed of many harmonics, using Fourier series  In complex (or Euler) representation, Fourier series coefficients X m are phasor components,

Han Q Le© Signal Fourier (or harmonic) Analysis (cont) If the signal is real (all cases involving real physical quantity), then:  Hence, we need to keep only positive frequencies  A signal can be represented by a plot of | X m | vs. frequency, or usually | X m | 2 if x(t) is voltage or current, known as the signal magnitude spectrum, or its power spectral density.  Equally important is the phase spectrum: plot of  m vs. frequency

Han Q Le© Do not be confused between the word “spectrum” in the general English sense vs. specific definition of “spectrum” in power spectral density, or phase spectrum.

Han Q Le© The Electromagnetic Spectrum Visible UV & solar blind

Han Q Le© Example of Spectra

Han Q Le© Example of Spectra

Han Q Le© Outline Review Signal analysis – Power spectral density Frequency response of a circuit – Transfer function – Bode plot Filters – Analog – Digital

Han Q Le© Example R C output v out [t] i(t)input v in [t] R C output v out [t] i(t) Frequency Response or, Frequency Transfer Function

Han Q Le© Frequency Transfer Function (Frequency Response Function) For many linear RLC circuits, the frequency response function usually has the form:

Han Q Le© Example: Test 1

Han Q Le© Bode Plot for Vout in Test 1

Han Q Le© Applications of Frequency Transfer Function Any signal can be decomposed as a sum of many phasors (Fourier components) For a linear system, each component can be multiplied by H[  ] to obtain the output phasor The signal output is simply the sum of all the individual phasor (Fourier component) outputs.

Han Q Le© Example R C input v in [t] output v out [t] i(t)

Han Q Le© Outline Review Signal analysis – Power spectral density Frequency response of a circuit – Transfer function – Bode plot Filters – Analog – Digital

Han Q Le© General Filter Concept Review This is a filterThis is also filterThis is another filter

Han Q Le© General Filter Concept A system (electronic circuit) can be designed such that its transfer function H[  ] has preference (let through) certain ranges of frequencies while attenuating (blocking) other frequencies Such a circuit is called a filter. Filter is a concept about the function of a circuit, not the circuit itself. Filter includes both amplitude response and phase shift. Usually, only amplitude is plotted.

Han Q Le© Common Types of Filters Low pass filter Band pass filter High pass filter Band stop (notch) filter

Han Q Le© Design of Filters A circuit designed to perform filtering function on an analog signal is called an analog filter. If a signal is digital (converted into a sequence of number), a filter can be realized as a mathematical operation, this is called digital filter. Digital filter can be done with any computing device: from a DSP chip to a computer.

Han Q Le© Example of Simple Analog Filters  RC band stop filter.  RC bandpass filters

Han Q Le© Example of Simple Analog Filters RLC resonant filter

Han Q Le© Example of Simple Analog Filters Notch filter application: rejection line 60-Hz signal

Han Q Le© Example: Test 1 Notch Filter

Han Q Le© Example: Test 1: Bandpass Filter

Han Q Le© Digital Filter Any filter function can be achieved with digital filter Micro- processor (DSP) Signal input User input Filtered signal output

Han Q Le© Digital Filter Digital filter can also be designed with sharp cut-off edge that is difficult with analog filter.