Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Digital Filter Designs for Recursive Frequency Analysis   Digital filters for recursively computing the discrete Fourier transform
(DFT) and estimating the frequency spectrum of sampled signals are examined,
with an emphasis on magnitude-response and numerical stability. In this
tutorial-style treatment, existing recursive techniques are reviewed, explained
and compared within a coherent framework; some fresh insights are provided and
new enhancements/modifications are proposed. It is shown that the replacement
of resonators by (non-recursive) modulators in sliding DFT (SDFT) analyzers
with either a finite impulse response (FIR), or an infinite impulse response
(IIR), does improve performance somewhat; however stability is not guaranteed,
as the cancellation of marginally stable poles by zeros is still involved. The
FIR deadbeat observer is shown to be more reliable than the SDFT methods, an
IIR variant is presented, and ways of fine-tuning its response are discussed. A
novel technique for stabilizing IIR SDFT analyzers with a fading memory, so
that all poles are inside the unit circle, is also derived. Slepian and
sum-of-cosine windows are adapted to improve the frequency responses for the
various FIR and IIR DFT methods.

11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph