Digital image processing for converting images from one sampling structure to another

A method of digital image processing in one or more digital image processors for achieving a transparent cascade on up conversion in the sampling rate ratio N:M where N and M are integers and subsequent M:N down conversion, where the up and down conversion ratios N:M and M:N respectively are rational numbers and the integers N and M satisfy the condition 1<N<M, wherein the up conversion filter operates on a sampled signal Sinput and is chosen to take the form Sup(n)=ΣSinput(k).g(Nn-Mk) where k is the running integer over which the sum is taken and wherein a corresponding down conversion filter operates on the up converted signal Sup and is chosen to take the form Sdown(n)=ΣSup(k).h(Mn-Nk);

• the pair (g, h) of up and down conversion filters being chosen so that Σh(Mn-Nk).g(Nk-Mm) is equal to unity if n=m and is otherwise equal to zero, and wherein every filtered sample is formed from a weighted sum of at least two input samples.

A method of digital image processing in one or more digital image processors for achieving a transparent cascade on up conversion in the sampling rate ratio N:M where N and M are integers and subsequent M:N down conversion, where the up and down conversion ratios N:M and M:N respectively are rational numbers and the integers N and M satisfy the condition 1<N<M, wherein the up conversion filter operates on a sampled signal Sinput and is chosen to take the form Sup(n)=ΣSinput(k).g(Nn-Mk) where k is the running integer over which the sum is taken and wherein a corresponding down conversion filter operates on the up converted signal Sup and is chosen to take the form Sdown(n)=ΣSup(k).h(Mn-Nk);

• the pair (g, h) of up and down conversion filters being chosen so that Σh(Mn-Nk).g(Nk-Mm) is equal to unity if n=m and is otherwise equal to zero, and wherein the frequency response of the up conversion filter is substantially the same as the frequency response of the down conversion filter.

A method of digital image processing in one or more digital image processors for achieving a transparent cascade on up conversion in the sampling rate ratio N:M where N and M are integers and subsequent M:N down conversion, where the up and down conversion ratios N:M and M:N respectively are rational numbers and the integers N and M satisfy the condition 1<N<M, wherein the up conversion filter operates on a sampled signal Sinput and is chosen to take the form Sup(n)=ΣSinput(k).g(Nn-Mk) where k is the running integer over which the sum is taken and wherein a corresponding down conversion filter operates on the up converted signal Sup and is chosen to take the form Sdown(n)=ΣSup(k).h(Mn-Nk);

• the pair (g, h) of up and down conversion filters being chosen so that Σh(Mn-Nk).g(Nk-Mm) is equal to unity if n=m and is otherwise equal to zero, and wherein the frequency response of the down converter at the sampling frequency of the sampled signal Sinput is less than 10%.

A digital image processing system in which first image data at a lower sampling frequency is up-sampled in a sampling ratio N:M to a higher sampling frequency in an up-sampling filter;

• and, second image data at the said higher sampling frequency is down-sampled in a sampling ratio M:N to the said lower sampling frequency in a down-sampling filter, where N and M are integers, where 1<N<M and where M is not a multiple of N, wherein a frequency response is optimised to minimise the reconstruction error due to the combination of the up-sampling filter and the down-sampling filter and wherein the filter aperture of the up-sampling filter and the filter aperture of the down-sampling filter are each constructed from said optimised frequency response.

A method of digital image processing in one or more digital image processors in which first image data at a lower sampling frequency is up-sampled in a sampling ratio N:M to a higher sampling frequency in an up-sampling filter;

• and, second image data at the said higher sampling frequency is down-sampled in a sampling ratio M:N to the said lower sampling frequency in a down-sampling filter where the combination of the up-sampling filter and the down-sampling filter is substantially transparent characterised, where N and M are integers, where 1<N<M and where M is not a multiple of N and wherein the frequency response of the down converter at the lower sampling frequency is less than 10%.

A non-transitory computer program product contained instructions adapted to cause programmable apparatus to implement a method of digital image processing for achieving a transparent cascade on up conversion in the sampling rate ratio N:M where N and M are integers and subsequent M:N down conversion, where the up and down conversion ratios N:M and M:N respectively are rational numbers and the integers N and M satisfy the condition 1<N<M, wherein the up conversion filter operates on a sampled signal Sinput and is chosen to take the form Sup(n)=ΣSinput(k).g(Nn-Mk) where k is the running integer over which the sum is taken and wherein a corresponding down conversion filter operates on the up converted signal Sup and is chosen to take the form Sdown(n)=ΣSup(k).h(Mn-Nk);

• the pair (g, h) of up and down conversion filters being chosen so that Σh(Mn-Nk).g(Nk-Mm) is equal to unity if n=m and is otherwise equal to zero, and wherein every filtered sample is formed from a weighted sum of at least two input samples.