Replies to post #47205 on Short Term Trading Member Forum

[Oddlot]

re band pass: what is the result if the cycle length is known only approximately, and the filter cutoff frequencies are wide enough to catch the unknown frequency. IE, a classic set is days: 130/65/32.5. If the cutoffs were 50 and 25, would your results be the same??
Oddlot

[techcharter]

DinDinDon Band Pass Filtering

I'm at the point in your last statement:

"At this moment, if you see magnitude starting to show resonant frequency, it is an evidence that the hutting cycle is active but there is NO EASY WAY TO GET RELIABLE QUANTITATIVE DATA."

I've been using Fourier analysis which is a single lowpass filter and a series of band pass filters whose center frequencies are harmonically related. Fourier series also fall into the larger Finite Impulse Response (window filters) filter catagory, which has no memory of past filter outputs. Butterworth and Cheby filters are typically represented as difference equations, making up the Infinite Impulse Response filter category, which has memory of past filter outputs. The data I posted was from a window filter of 15000 points that has 400 cosine cycles as filter coefficients. It is HIGHLY selective.

The graphs showing settling is a phenomena I regularly observe using bandpass filters of both types. I've been able to simulate this using an input signal with a constant amplitude and linearly varying frequency ( something like frequency modulation), or using an input signal of a constant frequency and varying amplitude (something like amplitude modulation). In reality, the market is doing both.

I'm back to where my original post asks, "What does it mean about the trend when the magnitude of the output of a bandpass filter over the positive half of the cycle is greater than the magnitude of the negative half of the cycle?"