MIT6_003S10_lec18

MIT6_003S10_lec18 - 6.003: Signals and Systems...

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6.003: Signals and Systems Discrete-Time Frequency Representations April 13, 2010
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Signals and/or Systems Two perspectives: feedback and control (focus on systems) + controller plant sensor X Y Is the system stable? signal processing (focus on signals) target image Learn about target ( signal ) from the image ( signal ). Fourier methods are especially useful in signal processing.
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Historical Perspective Broad range of CT signal-processing problems: audio radio (noise/static reduction, automatic gain control, etc.) telephone (equalizers, echo-suppression, etc.) hi-fi (bass, treble, loudness, etc.) television (brightness, tint, etc.) radar and sonar (sensitivity, noise suppression, object detection) ... Increasing important applications of DT signal processing: MP3 JPEG MPEG MRI
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Signal Processing: Acoustical Mechano-acoustic components to optimize frequency response of loudspeakers: e.g., “bass-reflex” system. driver reflex port
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Signal Processing: Acoustico-Mechanical Passive radiator for improved low-frequency preformance. driver passive radiator
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Signal Processing: Electronic The development of low-cost electronics enhanced our ability to alter the natural frequency responses of systems. 110 100 90 80 70 10 1 10 2 10 3 10 4 10 5 Frequency (Hz) Eight drivers faced the wall; one pointed faced the listener. Electronic “equalizer” compensates for limited frequency response. Magnitude (dB)
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Signal Processing Modern audio systems process sounds digitally. A/D DT filter D/A x ( t ) y ( t ) x [ n ] y [ n ]
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Signal Processing Modern audio systems process sounds digitally. AV SS(REF) V REFM REFP RFIL T DD SS DV Control AINRP AINRM AINLM AINLP 24-Bit Stereo ADC Controller 24-Bit Stereo DAC SDATA Control L L+R 32-Bit Audio Signal Processor R 32-Bit Audio Signal Processor OSC/CLK Select PLL Reference Voltage Supplies Analog Supplies Digital I 2 C Control Analog Format Output Logic Control Register AINRP AINRM RINA RINB AINLP AINLM Texas Instruments TAS3004 LINA LINB 2 channels SDOUT0 VCOM ALLPASS INPA AOUTL GPI5 24 bit ADC, 24 bit DAC GPI4 GPI3 AOUTR L+R SDOUT2 SDOUT1 48 kHz sampling rate GPI2 GPI1 GPI0 100 MIPS CS1 SDA SCL $7.70 ($4.81 in bulk) PWR_DN RESET TEST Courtesy of Texas Instruments. Used with permission. SDIN1 SDIN2 LRCLK/O SCLK/O IFM/S CLKSEL XT ALI/ MCLK ALO MCLKO CAP_PLL Figure 1- 1. TAS3004 Block Diagram
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DT Fourier Series and Frequency Response Today: frequency representations for DT signals and systems.
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± ± Complex Geometric Sequences Complex geometric sequences are eigenfunctions of DT LTI systems. n Find response of DT system ( h [ n ] ) to input x [ n ]= z . y [ n ]=( h x )[ n h [ k ] z n k = z n h [ k ] z k = H ( z ) z n . k = −∞ k = −∞ Complex geometrics (DT): analogous to complex exponentials (CT) h [ n ] z n H ( z ) z n h ( t ) e st st H ( s ) e
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Rational System Functions A system described by a linear difference equation with constant coefficients system function that is a ratio of polynomials in z .
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This note was uploaded on 12/14/2011 for the course EE 6.003 taught by Professor Freeman during the Fall '11 term at MIT.

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MIT6_003S10_lec18 - 6.003: Signals and Systems...

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