Obviously fresh foods spoil fastest (think produce, fish, meats and dairy) so they are replenished more quickly and the thin supply chain (field to fork) passes along increased costs fast. Processed foods have a longer shelf life (boxed, canned, frozen, etc), and as a consequence have a much larger inventory level in manufacturing, warehousing and retail storerooms/shelves. Within processed foods, there is a lag between cost increase at origination and that cost hitting the stores.
(Sundance) The Bureau of Labor and Statistics (BLS) released the August review [DATA HERE] of producer prices for last month. August rose 0.7% with cumulative results now showing an 8.3% increase in prices; the largest year-over-year jump in prices for final demand products in the history of tracking. The prior record was July with 7.8%.