NFourierTrigSeries and NFourierCoefficient
- To: mathgroup at smc.vnet.net
- Subject: [mg114356] NFourierTrigSeries and NFourierCoefficient
- From: zosi <zosi at to.infn.it>
- Date: Thu, 2 Dec 2010 05:38:06 -0500 (EST)
Dear All,
My problem is about NFourierTrigSeries
and NFourierCoefficient with V7 or V8.
(everything OK with V6, with adequate FourierParameters).
Suppose I have a very simple function, first defined in (-1,4)
in two ways: Case A), with /;
and Case B) with Piecewise
and then extended periodically.
Case A) (* it does work *)
tmin = -1; tmax = 4; (* the interval is asymmetric around origin *)
period = tmax - tmin;
g[t_] := (t - 1)^2 /; tmin <= t <= tmax
g[t_] := g[t - period] /; t > tmax
g[t_] := g[t + period] /; t < tmin
Plot[g[t], {t, tmin, 2 tmax + 1}]
Needs["FourierSeries`"]
b = Solve[(2 \[Pi] )/bb == period, bb][[1, 1, 2]]
a = 1;
sergNTrig = NFourierTrigSeries[g[t], t, 7,
FourierParameters -> {a,b}] // Simplify
Plot[{g[t], sergNTrig}, {t, tmin, 2 tmax + 1}] (* good reconstruction *)
Case B) (* it fails *)
(* I just use Piecewise instead of :; *)
tmin = -1; tmax = 4;
period = tmax - tmin;
h[t_] := Piecewise[{{(t - 1)^2, tmin <= t <= tmax}}]
h[t_] := h[t - period] /; t > tmax
h[t_] := h[t + period] /; t < tmin
Needs["FourierSeries`"]
b = Solve[(2 \[Pi] )/bb == period, bb][[1, 1, 2]]
a = 1;
serhNTrig = NFourierTrigSeries[h[t], t, 7,
FourierParameters -> {a, b}] // Simplify
Plot[{h[t], serhNTrig}, {t, tmin, 2 tmax + 1}] (* reconstruction fails *)
*)
Finally, **in both cases** I am not able to find the
right parameters (i.e., coefmul and {a,b}) in, e.g.,
direct$coeff = Table[coefmul*NFourierCoefficient[h[t], t, n,
FourierParameters -> {a,b}], {n, 0, 7}]
to obtain directly the Fourier coefficients.
Where am I wrong ?
Many thanks for your help.
Gianfranco Zosi
Dip Fisica Generale
University of Turin