Fast filtering means and filtering and decimation methods
The invention relates to a hardware implemented filtering method including establishing a representation DIS of the derivative of at least a part of a time-quantized input signal IS, and establishing at least one sample of a time- and amplitude-quantized output signal OS by performing filtering on the basis of at least a part of a filter representation IFC 1 , IFC 2 , IFC 3 and the representation DIS of the derivative of at least a part of the input signal IS. The invention further relates to a hardware implemented decimation method for decimating a time-quantized input signal IS including dividing the time-quantized input signal IS into intervals, for each of the intervals establishing a sample of a time- and amplitude-quantized output signal OS according to the above mentioned filtering method. The invention further relates to a fast filtering means FFM implementing the above-mentioned methods.
1. Hardware implemented filtering method comprising:
establishing a representation of a derivative of at least a part of a time-quantized pulse width modulated input signal, and
establishing at least one sample of a time- and amplitude-quantized pulse code modulated output signal by performing filtering on the basis of at least a part of a filter representation and said representation of the derivative of at least a part of said input signal;
whereby said performing filtering is arranged to omit arithmetic operations involving such samples of said representation of the derivative of at least a part of said input signal that are derived from identically valued continguous samples of said time-quantized input signal.
2. Hardware implemented filtering method according to claim 1 , whereby said establishing at least one sample of a time- and amplitude-quantized output signal is implemented according to a hardware implemented method of convolving in a time domain an input signal with an impulse response in order to establish an output signal, comprising:
providing said output signal at least partly by a convolution in the time domain of a difference signal representation of said input signal and a sum representation of said impulse response.
3. Hardware implemented filtering method according to claim 2 , whereby said impulse response is finite.
4. Hardware implemented filtering method according to claim 1 , whereby said time-quantized input signal comprises in average at least 10 samples for each input signal value change.
5. Hardware implemented filtering method according to claim 1 , whereby said establishing a representation of the derivative of at least a part of said time-quantized input signal comprises establishing a sequence of differences between successive samples of said at least a part of said input signal.
6. Hardware implemented filtering method according to claim 1 , whereby said at least a part of said time-quantized input signal in respect of its length corresponds to the length of said at least a part of an impulse response.
7. Hardware implemented filtering method according to claim 1 , whereby said representation of the derivative of at least a part of said time-quantized input signal is stored in a differentiated input signal representing array.
8. Hardware implemented filtering method according to claim 1 , whereby said establishing a representation of the derivative of at least a part of a time-quantized input signal comprises indexing corresponding times and directions of amplitude changes of said at least a part of said input signal.
9. Hardware implemented filtering method according to claim 1 , whereby the length of said at least a part of said filter representation is an integer multiple of the length of a symbol of said at least a part of said time-quantized input signal.
10. Hardware implemented filtering method according to claim 1 , whereby a number of changes within a symbol of said at least a part of said time-quantized input signal is constant.
11. Hardware implemented filtering method according to claim 1 , whereby said times are indexed relative to each other.
12. Hardware implemented filtering method according to claim 1 , whereby said establishing a representation of the derivative of at least a part of a time-quantized input signal comprises storing into a snapshot register said at least a part of said time-quantized input signal.
13. Hardware implemented filtering method according to claim 1 , whereby said establishing a representation of the derivative of at least a part of a time-quantized input signal comprises querying said snapshot register regarding input signal changes.
14. Hardware implemented filtering method according to claim 1 , whereby said at least a part of said filter representation is a sum representation of at least a part of an impulse response.
15. Hardware implemented filtering method according to claim 1 , whereby said at least a part of said filter representation is predetermined.
16. Hardware implemented filtering method according to claim 1 , whereby said at least a part of said filter representation is implemented by means of at least one filter coefficient.
17. Hardware implemented filtering method according to claim 1 , whereby said at least a part of said filter representation is implemented by means of at least one model, comprising at least one polynomial.
18. Hardware implemented filtering method according to claim 1 , whereby said implementation of said at least a part of said filter representation is adapted to utilize any symmetry of said filter representation.
19. Hardware implemented filtering method according to claim 1 , whereby said at least a part of said filter representation is user-adjustable.
20. Hardware implemented filtering method according to claim 1 , whereby said performing filtering comprises convolving said at least a part of said filter representation with said representation of the derivative of at least a part of said time-quantized input signal.
21. Hardware implemented filtering method according to claim 20 , whereby said convolving said at least a part of said filter representation with said representation of the derivative of at least a part of said time-quantized input signal is performed for only some of the samples of said time-quantized input signal.
22. Hardware implemented filtering method according to claim 1 , whereby said performing filtering further comprises for each of said at least one sample of a time- and amplitude-quantized output signal adding the result of multiplying an initial value of said at least a part of said time-quantized input signal with a value of said at least a part of said filter representation.
23. Hardware implemented filtering method according to claim 1 , whereby said performing filtering further comprises adding, for each of said at least one sample of a time- and amplitude-quantized output signal, an initial value of said at least a part of said time-quantized input signal.
24. Hardware implemented filtering method according to claim 1 , whereby said performing filtering comprises exercising the expression
y
[
n
]
=
∑
k
=
0
N
-
2
(
l
[
k
]
·
x
′
[
n
-
k
]
)
+
l
[
N
-
1
]
·
x
[
n
-
(
N
-
1
)
]
,
where y[n] represents said at least one sample of a time- and amplitude-quantized output signal, x[n] represents said at least a part of said time-quantized input signal, x′[n] represents said representation of the derivative of x[n], l[k] represents said at least a part of said filter representation, N represents the length of l[k].
25. Hardware implemented filtering method according to claim 1 , whereby said performing filtering further comprises performing conventional filtering.
26. Hardware implemented filtering method according to claim 1 , whereby a sample rate of said time- and amplitude-quantized output signal is different from a sample rate of said time-quantized input signal.
27. Hardware implemented filtering method according to claim 1 , whereby a sample rate of said time- and amplitude-quantized output signal corresponds to a symbol rate of said time-quantized input signal.
28. Hardware implemented filtering method according to claim 1 , whereby said filter representation comprises a sum representation of a low-pass filter.
29. Hardware implemented filtering method according to claim 1 , whereby said method is exercised in real time.
30. Hardware implemented filtering method according to claim 1 , whereby said at least a part of a filter representation represents at least a part of an impulse response.
31. Hardware implemented filtering method according to claim 1 , whereby said at least a part of a filter representation represents the derivative of at least a part of an impulse response.
32. Hardware implemented filtering method according to claim 1 further comprising the step of
integrating at least once said time- and amplitude-quantized output signal.
33. Hardware implemented decimation method for decimating a time-quantized pulse width modulated input signal comprising:
dividing said time-quantized input signal into intervals, for each of said intervals establishing a sample of a time- and amplitude-quantized pulse code modulated output signal by performing filtering on the basis of at least a part of a filter representation and a representation of a derivative of at least a part of said input signal;
whereby said performing filtering is arranged to omit arithmetic operations involving such samples of said representation of the derivative of at least a part of said input signal that are derived from identically valued continguous samples of said time-quantized input signal.
34. A filter arrangement comprising:
a differentiator for establishing a representation of a derivative of at least a part of a time-quantized pulse width modulated input signal, and
a filtering unit for establishing at least one sample of pulse code modulated output signal by performing filtering on the basis of at least a part of a filter representation and said representation of the derivative of at least a part of said input signal;
wherein said filtering unit is arranged to omit arithmetic operations involving such samples of said representation of the derivative of at least a part of said input signal that are derived from identically valued contiguous samples of said time-quantized input signal.