The A37's noise profile for JPEGs looks as you'd expect for a camera in this class: ISO 100 and 200 look good, you start to see artifacts at ISO 400, and the images are usable, depending upon content, up through ISO 3200.
You can see the noise mottling in the sky and the detail degradation on the clock, but this would be quite usable scaled down a little. Also, a lot of shots of the clock face taken with other cameras/lenses display serious fringing on the high-contrast edges; here it's not a problem. I'm not sure if it's doing correction in-camera, though.
(1/80, f5, ISO 1600, spot meter, AWB, 18-135mm lens at 55mm)