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Rate-changing appears expensive computationally, since for both decimation and interpolation the lowpass filter is implementedat the higher rate. However, this is not necessary.

Interpolation

For the interpolator, most of the samples in the upsampled signal are zero, and thus require no computation. ( [link] )

For m L m L m L and p m L ,
x 1 m m N 1 N 2 h L p m y m k N 1 L N 2 L g p k x 0 m L k
g p n h L n p Pictorially, this can be represented as in [link] .
These are called polyphase structures , and the g p n are called polyphase filters .

Computational cost

If h m is a length- N filter:
  • No simplification: N T 1 L N T 0 computations sec
  • Polyphase structure: L L N 1 T 0 o computations sec N T 0 where L is the number of filters, N L is the taps/filter, and 1 T 0 is the rate.
Thus we save a factor of L by not being dumb.
For a given precision, N is proportional to L , (why?), so the computational cost does increase with the interpolationrate.
Can similar computational savings be obtained with IIR structures?

Efficient decimation structures

We only want every M th output, so we compute only the outputs of interest. ( [link] ) x 1 m k N 1 N 2 x 0 L m k h k

Polyphase decimation structure

The decimation structures are flow-graph reversals of the interpolation structure. Although direct implementation ofthe full filter for every M th sample is obvious and straightforward, these polyphasestructures give some idea as to how one might evenly partition the computation over M cycles.

Efficient l/m rate changers

Interpolate by L and decimate by M ( [link] ).

Combine the lowpass filters ( [link] ).
We can couple the lowpass filter either to the interpolator or the decimator to implement it efficiently ( [link] ).
Of course we only compute the polyphase filter output selected by the decimator.

Computational cost

Every T 1 M L T 0 seconds , compute one polyphase filter of length N L , or N L T 1 N L M L T 0 N M T 0 multiplies second However, note that N is proportional to L M .

Questions & Answers

physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
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Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
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ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
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Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
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Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
what is learning? discuss how any three scholars propounded on how learning is
Grace Reply
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Source:  OpenStax, Dspa. OpenStax CNX. May 18, 2010 Download for free at http://cnx.org/content/col10599/1.5
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