ADC frequency response: confused about sinc filter

Question

I can't understand digital filters inside ADC.... 
 Modulators (sigma-delta) works with higher frequencies than the output data rate, so I need low-pass filter before decimation. Ok, it's clear. 
 Let's say I have a vibration sensor, range DC to 4kHz, frequency response as 2th order low-pass filter with pole at (-3dB) 4kHz, so flat frequency response until cut-off frequency. I need ODR at 1000SPS, 24 bit, so sigma-delta or SAR ADC, let's suppose 1000 SPS would be available from ADC as ODR decimation factor. Taking a look to available ADCs I always see sinc as digital filter after modulator (except for LTC2500).... but sinc filter hasn't flat response (AN-0979, fig.1-2, LTC2500 datasheet, fig.27), so I will not expect flat frequency response from ADC at selected ODR. AD7766 (AD7766 datasheet, fig. 32, 33, 34) shows flat response, so I suppose it would be overall frequency response including sinc, right? I am confused about sinc after modulator and flat frequency response I can find on datasheets.... 
 
 BTW: LTC2500 sinc filter coefficients are correct? I can see only ones....

NathanT · Accepted Answer

Hi Killertechno , 
 
 You can refer to this, as sincN filter has the following equation: 
 
 Where N is the order of the sinc filter and DF is down sampling factor. If for example, we calculate the coefficients for sinc1 and DF=4 then we can yield the following equation: 
 
 So, yes. The coefficients for Sinc1 are all 1s.)

JEstayo · Answer

Hi Killertechno , 
 Please take note that if your input signal can reach up to 4kHz, the ODR must be twice or greater. 
 Regarding the frequency response of the filters, the figures 32, 33, and 34 are showing the overall frequency response up to the ODR. 
 The sinc filter response you are referring to showing notches are plotted in multiples of the ODR, e.g. ODR, 2ODR, 3ODR. 
 
 Hi NathanT , Please help advise on the LTC2500 sinc filter coefficients. 
 Thanks, Janine

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ADC frequency response: confused about sinc filter

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