090112HomeWork1

090112HomeWork1 - ECE 700 Digital Signal Processing Winter...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE 700 Digital Signal Processing Winter 2009 Home Work 1 Due 1/21/09 PART I 1. A continuous-time signal x a ( t ) is the sum of unit amplitude sine waves of frequencies 300 Hz, 500 Hz, 1.2 kHz, 2.15 kHz, and 3.5 kHz. x a ( t ) is sampled at 2.5 kHz, leading to the discrete time signal x [ n ]. x [ n ] is then converted to the continuous-time with an ideal low- pass filter with a cut-off frequency of 1.0 kHz leading to the signal y a ( t ). The arrangement is shown in the figure below. What are the frequencies (in Hz) and amplitudes of the components present in y a ( t )? 2. Show that the upsampler and downsampler operators, 2 and commute. 3 3. Suppose x c ( t ) is bandlimited to 1.25/ T , and x 0 [ n ] = x c ( nT ), x 1 [ n ] = x c ( nT - T /3) and x 2 [ n ] = x c ( nT - 2 T /3). Design the black box below and show the corresponding details of the sinc reconstruction so that y c ( t ) = x c ( t ) i.e., x c ( t ) is perfectly recovered. 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4. For each of the following H ( z ), derive closed-form expressions for the R = 2 polyphase components, H 0 ( z ) and H 1 ( z ).
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

090112HomeWork1 - ECE 700 Digital Signal Processing Winter...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online