Which amplifier is good

I believe the original Sanyo STK 4231 is discontinued and is not recommended for 4 ohm loads like your Kenwood/Awai speakers.

That leaves you with the Class D choice which is 4 ohm capable: 2 × 50 W into a 4 Ω BTL load at 21 V (TPA3116D2).

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If you are asking if the TPA3116 has DSP built in, then the answer is no.

Digital Signal Processing (DSP) can allow you to adjust the EQ, i.e., amplify or lower the level of certain frequencies.

The amp shown in the image above includes volume, bass and treble controls, but not DSP.

DSP can also be used for room correction, i.e., to make sure that the sound is optimised for the size and shape of your room.
 
From the link, it looks like the DSP is automatically applied and there is no user control. Alternatively, the DSP labelling could be marketing hype!

I've never used one of these devices, but presumably the amplifier package will come with instructions should you choose to buy it.
 

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