Minimum Data Length for Integer Period Estimation

Tenneti, Srikanth V.; Vaidyanathan, P.P.

doi:10.1109/tsp.2018.2818080

Cited by 14 publications

(18 citation statements)

References 47 publications

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“…So Q = 15 and A has Φ(15) = 72 columns. It can be shown (from Theorem 9 in [23]) that L min = 56 in this case. With N = L min , A is a fat matrix of size 56 × 72.…”

Section: (B) Unique Identifiability Of Periods Using the Farey Dictiomentioning

confidence: 86%

“…where s 0 = number of non-zero elements in s. It is shown in [23] that the support of this solution is equal to the support of the ideal solution s (I) as long as N ≥ L min where the threshold L min is derived in [23]. (This is true regardless of whether the sparsest solution is unique or not.)…”

Section: (B) Unique Identifiability Of Periods Using the Farey Dictiomentioning

confidence: 99%

“…Q} then the period of x(n) itself may not belong in this set. In this case, L min has a more complicated expression, and it is given in Theorem 9 of [23].…”

Section: (B) Unique Identifiability Of Periods Using the Farey Dictiomentioning

confidence: 99%

“…So the number of columns in the dictionary should be at least Φ(Q). As explained in §4b, the minimum number of rows required L min has also been derived in [23,33]. This gives the number of samples necessary to identify periods using dictionary methods.…”

Section: Minimum Data Length For Integer Period Estimationmentioning

confidence: 99%

“…required, in order to identify P through any computational means at all (not necessarily using the above dictionaries)? It is shown in [23] that…”

Section: Minimum Data Length For Integer Period Estimationmentioning

confidence: 99%

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Srinivasa Ramanujan and signal-processing problems

Vaidyanathan

Tenneti

2019

Phil. Trans. R. Soc. A.

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The Ramanujan sum c q ( n ) has been used by mathematicians to derive many important infinite series expansions for arithmetic-functions in number theory. Interestingly, this sum has many properties which are attractive from the point of view of digital signal processing. One of these is that c q ( n ) is periodic with period q , and another is that it is always integer-valued in spite of the presence of complex roots of unity in the definition. Engineers and physicists have in the past used the Ramanujan-sum to extract periodicity information from signals. In recent years, this idea has been developed further by introducing the concept of Ramanujan-subspaces. Based on this, Ramanujan dictionaries and filter banks have been developed, which are very useful to identify integer-valued periods in possibly complex-valued signals. This paper gives an overview of these developments from the view point of signal processing. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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“…So Q = 15 and A has Φ(15) = 72 columns. It can be shown (from Theorem 9 in [23]) that L min = 56 in this case. With N = L min , A is a fat matrix of size 56 × 72.…”

Section: (B) Unique Identifiability Of Periods Using the Farey Dictiomentioning

confidence: 86%

Section: (B) Unique Identifiability Of Periods Using the Farey Dictiomentioning

confidence: 99%

“…Q} then the period of x(n) itself may not belong in this set. In this case, L min has a more complicated expression, and it is given in Theorem 9 of [23].…”

Section: (B) Unique Identifiability Of Periods Using the Farey Dictiomentioning

confidence: 99%

Section: Minimum Data Length For Integer Period Estimationmentioning

confidence: 99%

“…required, in order to identify P through any computational means at all (not necessarily using the above dictionaries)? It is shown in [23] that…”

Section: Minimum Data Length For Integer Period Estimationmentioning

confidence: 99%

See 3 more Smart Citations

Srinivasa Ramanujan and signal-processing problems

Vaidyanathan

Tenneti

2019

Phil. Trans. R. Soc. A.

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Stagger period estimation algorithm for multiple sets of radar pulses

et al. 2020

IET Radar, Sonar & Navigation

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Period and signal reconstruction from the curve of trains of samples

Rupniewski

2021

IET Signal Processing

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A sequence of samples of a periodic signal can be treated as a point in a multi-dimensional space. All such sequences of a given length and taken at a given sampling rate form a closed curve. We prove that this curve determines the period of the sampled signal, even if the sequences are of short length and are taken at a sub-Nyquist rate. This result is obtained with a help of the theory of rotation numbers developed by Poincar. We also prove that the curve of sample-sequences determines the sampled signal up to a time shift provided that the ratio of the sampling period to the period of the signal is irrational. Eventually, we give an example, which shows that the same is not true if this ratio is rational.

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Minimum Data Length for Integer Period Estimation

Cited by 14 publications

References 47 publications

Srinivasa Ramanujan and signal-processing problems

Srinivasa Ramanujan and signal-processing problems

Stagger period estimation algorithm for multiple sets of radar pulses

Period and signal reconstruction from the curve of trains of samples

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