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y := α * (y[i-1] + x - x[i-1])
y := y[i-1] + α * (x - y[i-1])
Your system is basically a band pass filter,
A repetitive half sine would be like the output of a full wave rectifier. Sorry for the lack of clarity.
I believe that you have mis-understood the experiment. This has nothing to do with filters. I am trying to show you a whole new way to look at radio.
The "hump" is 180 degrees of one frequency.
Quote from: Hayseed on 30/10/2019 16:48:51The "hump" is 180 degrees of one frequency. No it is not.What would you expect to get if I put a half wave rectified sine wave into a spectrum analyser?
Your system is basically a band pass filter, which is a combination of high pass filter and low pass filter.You can simulate it using spreadsheet such as Excel file following the formula for HPF and LPF.https://en.wikipedia.org/wiki/High-pass_filter#Algorithmic_implementationQuotey := α * (y[i-1] + x - x[i-1])https://en.wikipedia.org/wiki/Low-pass_filter#Simple_infinite_impulse_response_filterQuotey := y[i-1] + α * (x - y[i-1])here is step by step procedure to make the simulation:Open the spreadsheet.type following formulas into the corresponding cells.B1 : =PI()/40this cell determine the periodC1 : 0.5this cell determine the value of α for HPFD1 : 0.1this cell determine the value of α for LPFA2 : iB2 : inputC2 : HPFD2 : LPFE2 : HLPFF2 : LHPFA3 to F3 : 0A4 to A 243 : integer from 1 to 240B4 : =ABS(SIN(A4*$B$1))this is the formula to generate half sinewave signalC4: =$C$1*(C3-B3+B4)this is the formula to produce HPF of the input signalD4: =D3+$D$1*(B4-D3)this is the formula to produce LPF of the input signalE4 : =E3+$D$1*(C4-E3)this is the formula to show the result if the input signal is fed to HPF first, and then LPFF4 : =$C$1*(F3-D3+D4)this is the formula to show the result if the input signal is fed to LPF first, and then HPFCopy the cells B4 to F4, then paste into cells B5 to B243You'll find that the results in column E equal those in column F. This shows that those functions are commutative.To get visual representation, just select the cells A2 to F243. From command menu select insert>scatter(X,Y) chartYou can see how the variables in cells B1 to D1 change the shape of the curves. They represents simplified linear combination of the antennas and electronic circuitries of your transmitter and receiver.
Excuse me interrupting (as a non-expert) but is this topic related to Single Sideband Transmission? As invented by radio hams decades ago?